Physics Problems with Solutions
Velocity and speed: solutions to problems.
A man walks 7 km in 2 hours and 2 km in 1 hour in the same direction. a) What is the man's average speed for the whole journey? b) What is the man's average velocity for the whole journey? Solution to Problem 1: a)
| = 3 km/h |
| = 3 km/h |
| = 3.2 km/h (approximated to the nearest tenth) |
| = 1.5 km/h |
You start walking from a point on a circular field of radius 0.5 km and 1 hour later you are at the same point. a) What is your average speed for the whole journey? b) What is your average velocity for the whole journey? Solution to Problem 3: a) If you walk around a circular field and come back to the same point, you have covered a distance equal to the circumference of the circle.
| = Pi km/h = 3.14 km/h (approximated) |
John drove South 120 km at 60 km/h and then East 150 km at 50 km/h. Determine a) the average speed for the whole journey? b) the magnitude of the average velocity for the whole journey? Solution to Problem 4: a)
| = 54 km/h |
| = 38.4 km/h (approximated) |
If I can walk at an average speed of 5 km/h, how many miles I can walk in two hours? Solution to Problem 5: distance = (average speed) * (time) = 5 km/h * 2 hours = 10 km using the rate of conversion 0.62 miles per km, the distance in miles is given by distance = 10 km * 0.62 miles/km = 6.2 miles
A train travels along a straight line at a constant speed of 60 mi/h for a distance d and then another distance equal to 2d in the same direction at a constant speed of 80 mi/h. a)What is the average speed of the train for the whole journey?
| = 72 mi/h |
A car travels 22 km south, 12 km west, and 14 km north in half an hour. a) What is the average speed of the car? b) What is the final displacement of the car? c) What is the average velocity of the car?
Solution to Problem 7: a)
| = 96 km/h |
| = 28.8 km/h (approximated) |
Solution to Problem 8: a)
| = 2 m/s |
| = 1.5 m/s (approximated) |
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 Want to create or adapt books like this? Learn more about how Pressbooks supports open publishing practices. Chapter 8: Rational Expressions 8.8 Rate Word Problems: Speed, Distance and TimeDistance, rate and time problems are a standard application of linear equations. When solving these problems, use the relationship rate (speed or velocity) times time equals distance . [latex]r\cdot t=d[/latex] For example, suppose a person were to travel 30 km/h for 4 h. To find the total distance, multiply rate times time or (30km/h)(4h) = 120 km. The problems to be solved here will have a few more steps than described above. So to keep the information in the problem organized, use a table. An example of the basic structure of the table is below:
The third column, distance, will always be filled in by multiplying the rate and time columns together. If given a total distance of both persons or trips, put this information in the distance column. Now use this table to set up and solve the following examples. Example 8.8.1 Joey and Natasha start from the same point and walk in opposite directions. Joey walks 2 km/h faster than Natasha. After 3 hours, they are 30 kilometres apart. How fast did each walk?
The distance travelled by both is 30 km. Therefore, the equation to be solved is: [latex]\begin{array}{rrrrrrl} 3r&+&3(r&+&2)&=&30 \\ 3r&+&3r&+&6&=&30 \\ &&&-&6&&-6 \\ \hline &&&&\dfrac{6r}{6}&=&\dfrac{24}{6} \\ \\ &&&&r&=&4 \text{ km/h} \end{array}[/latex] This means that Natasha walks at 4 km/h and Joey walks at 6 km/h. Example 8.8.2 Nick and Chloe left their campsite by canoe and paddled downstream at an average speed of 12 km/h. They turned around and paddled back upstream at an average rate of 4 km/h. The total trip took 1 hour. After how much time did the campers turn around downstream?
The distance travelled downstream is the same distance that they travelled upstream. Therefore, the equation to be solved is: [latex]\begin{array}{rrlll} 12(t)&=&4(1&-&t) \\ 12t&=&4&-&4t \\ +4t&&&+&4t \\ \hline \dfrac{16t}{16}&=&\dfrac{4}{16}&& \\ \\ t&=&0.25&& \end{array}[/latex] This means the campers paddled downstream for 0.25 h and spent 0.75 h paddling back. Example 8.8.3 Terry leaves his house riding a bike at 20 km/h. Sally leaves 6 h later on a scooter to catch up with him travelling at 80 km/h. How long will it take her to catch up with him?
The distance travelled by both is the same. Therefore, the equation to be solved is: [latex]\begin{array}{rrrrr} 20(t)&=&80(t&-&6) \\ 20t&=&80t&-&480 \\ -80t&&-80t&& \\ \hline \dfrac{-60t}{-60}&=&\dfrac{-480}{-60}&& \\ \\ t&=&8&& \end{array}[/latex] This means that Terry travels for 8 h and Sally only needs 2 h to catch up to him. Example 8.8.4 On a 130-kilometre trip, a car travelled at an average speed of 55 km/h and then reduced its speed to 40 km/h for the remainder of the trip. The trip took 2.5 h. For how long did the car travel 40 km/h?
[latex]\begin{array}{rrrrrrr} 55(t)&+&40(2.5&-&t)&=&130 \\ 55t&+&100&-&40t&=&130 \\ &-&100&&&&-100 \\ \hline &&&&\dfrac{15t}{15}&=&\dfrac{30}{15} \\ \\ &&&&t&=&2 \end{array}[/latex] This means that the time spent travelling at 40 km/h was 0.5 h. Distance, time and rate problems have a few variations that mix the unknowns between distance, rate and time. They generally involve solving a problem that uses the combined distance travelled to equal some distance or a problem in which the distances travelled by both parties is the same. These distance, rate and time problems will be revisited later on in this textbook where quadratic solutions are required to solve them. For Questions 1 to 8, find the equations needed to solve the problems. Do not solve.
Solve Questions 9 to 22.
Answer Key 8.8 Intermediate Algebra Copyright © 2020 by Terrance Berg is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted. Share This BookHome of Science Speed, Velocity, and Acceleration ProblemsWhat is speed. Speed, S = Distance (d) / Time (t) The S.I unit for speed is meter per second (m/s) or ms -1 Non-Uniform or Average Speed : This is a non-steady distance covered by an object at a particular period of time. We can also define non-uniform speed as the type of distance that an object covered at an equal interval of time. Actual speed: This is also known as the instantaneous speed of an object which is the distance covered by an object over a short interval of time. You may also like to read: What is Velocity?Definition of Velocity: Velocity is the rate of displacement with time. Velocity is the speed of an object in a specified direction. The unit of velocity is the same as that of speed which is meter per second (ms -1 ). We use V as a symbol for velocity. Uniform VelocityDefinition of uniform velocity: The rate of change of displacement is constant no matter how small the time interval may be. Also, uniform velocity is the distance covered by an object in a specified direction in an equal time interval. What is Acceleration?Uniform acceleration, what is retardation, equations of motion, solved problems of speed, velocity, and acceleration. Here are solved problems to help you understand how to calculate speed, velocity, and acceleration: Distance = 15 m/s x 15 s = 225 m Final velocity, v = speed = 108 km/h = (108 x 1000m) / (60 x 60s) = 108,000/3,600 = 30m/s Acceleration = change in velocity/ time = (v-u)/t = (30-0)/15 =30/15 = 2ms -2 Time taken = 1 hour = 1 x 60 x 60s =3,600s Initial displacement of the car = 80km The time for 80km is 1hr Average velocity = total displacement/total time taken = 100km/2hrs = 50km/h and How to Calculate Velocity Ratio of an Inclined Plane and we can apply the formula for acceleration that says Note: The acceleration due to the gravity of a body on the surface of the earth is constant (9.8ms -2 ), even though there may be a slight difference due to the mass and altitude of the body. maximum height = displacement = 50m a = (0 – 10 2 )/(2 x 50) = -100/100 = -1 ms -2 Note: Retardation is the negative of acceleration, thus it is written in negative form. Distance, s =? s = ut + (1/2)at 2 s = 32 + (1/2) x 80 = 32 + 40 = 72m Final velocity, v = 0 We already know that acceleration, a = change in velocity/time A body is traveling at a velocity of 20 m/s and has a mass of 10 kg. How much force is required to change its velocity by 10 m/s in 5 seconds? Share this post: on Twitter on Facebook on Google+ How to Calculate Cost of Electricity Per kwhHow to calculate centripetal force. Problems on Calculating Speed Here we will learn to solve different types of problems on calculating speed. We know, the speed of a moving body is the distance traveled by it in unit time. Formula to find out speed = distance/time Word problems on calculating speed: 1. A man walks 20 km in 4 hours. Find his speed. Solution: Distance covered = 20 km Time taken = 4 hours We know, speed = distance/time = 20/4 km/hr Therefore, speed = 5 km/hr 2. A car covers a distance of 450 m in 1 minute whereas a train covers 69 km in 45 minutes. Find the ratio of their speeds. Speed of car = Distance covered/Time taken = 450/60 m/sec = 15/2 = 15/2 × 18/5 km/hr = 27 km/hr Distance covered by train = 69 km Time taken = 45 min = 45/60 hr = 3/4 hr Therefore, speed of trains = 69/(3/4) km/hr = 69/1 × 4/3 km/hr = 92 km/hr Therefore, ratio of their speed i.e., speed of car/speed of train = 27/92 = 27 : 92 3. Kate travels a distance of 9 km from her house to the school by auto-rickshaw at 18 km/hr and returns on rickshaw at 15 km/hr. Find the average speed for the whole journey. Time taken by Kate to reach school = distance/speed = 9/18 hr = 1/2 hr Time taken by Kate to reach house to school = 9/15 = 3/5 hr Total time of journey = (1/2 + 3/5) hr Total time of journey = (5 + 6)/10 = 11/10 hr Total distance covered = (9 + 9) km = 18 km Therefore, average speed for the whole journey = distance/speed = 18/(11/10) km/hr = 18/1 × 10/11 = (18 × 10)/(1 × 11) km/hr = 180/11 km/hr = 16.3 km/hr (approximately) Speed of Train Relationship between Speed, Distance and Time Conversion of Units of Speed Problems on Calculating Distance Problems on Calculating Time Two Objects Move in Same Direction Two Objects Move in Opposite Direction Train Passes a Moving Object in the Same Direction Train Passes a Moving Object in the Opposite Direction Train Passes through a Pole Train Passes through a Bridge Two Trains Passes in the Same Direction Two Trains Passes in the Opposite Direction 8th Grade Math Practice From Problems on Calculating Speed to HOME PAGE Didn't find what you were looking for? 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Solved Speed, Velocity, and Acceleration ProblemsSimple problems on speed, velocity, and acceleration with descriptive answers are presented for the AP Physics 1 exam and college students. In each solution, you can find a brief tutorial. Speed and velocity Problems:Problem (1): What is the speed of a rocket that travels $8000\,{\rm m}$ in $13\,{\rm s}$? Solution : Speed is defined in physics as the total distance divided by the elapsed time, so the rocket's speed is \[\text{speed}=\frac{8000}{13}=615.38\,{\rm m/s}\] Problem (2): How long will it take if you travel $400\,{\rm km}$ with an average speed of $100\,{\rm m/s}$? Solution : Average speed is the ratio of the total distance to the total time. Thus, the elapsed time is \begin{align*} t&=\frac{\text{total distance}}{\text{average speed}}\\ \\ &=\frac{400\times 10^{3}\,{\rm m}}{100\,{\rm m/s}}\\ \\ &=4000\,{\rm s}\end{align*} To convert it to hours, it must be divided by $3600\,{\rm s}$ which gives $t=1.11\,{\rm h}$. Problem (3): A person walks $100\,{\rm m}$ in $5$ minutes, then $200\,{\rm m}$ in $7$ minutes, and finally $50\,{\rm m}$ in $4$ minutes. Find its average speed. Solution : First find its total distance traveled ($D$) by summing all distances in each section, which gets $D=100+200+50=350\,{\rm m}$. Now, by definition of average speed, divide it by the total time elapsed $T=5+7+4=16$ minutes. But keep in mind that since the distance is in SI units, so the time traveled must also be in SI units, which is $\rm s$. Therefore, we have\begin{align*}\text{average speed}&=\frac{\text{total distance} }{\text{total time} }\\ \\ &=\frac{350\,{\rm m}}{16\times 60\,{\rm s}}\\ \\&=0.36\,{\rm m/s}\end{align*} Problem (4): A person walks $750\,{\rm m}$ due north, then $250\,{\rm m}$ due east. If the entire walk takes $12$ minutes, find the person's average velocity. Solution : Average velocity , $\bar{v}=\frac{\Delta x}{\Delta t}$, is displacement divided by the elapsed time. Displacement is also a vector that obeys the addition vector rules. Thus, in this velocity problem, add each displacement to get the total displacement . In the first part, displacement is $\Delta x_1=750\,\hat{j}$ (due north) and in the second part $\Delta x_2=250\,\hat{i}$ (due east). The total displacement vector is $\Delta x=\Delta x_1+\Delta x_2=750\,\hat{i}+250\,\hat{j}$ with magnitude of \begin{align*}|\Delta x|&=\sqrt{(750)^{2}+(250)^{2}}\\ \\&=790.5\,{\rm m}\end{align*} In addition, the total elapsed time is $t=12\times 60$ seconds. Therefore, the magnitude of the average velocity is \[\bar{v}=\frac{790.5}{12\times 60}=1.09\,{\rm m/s}\] Problem (5): An object moves along a straight line. First, it travels at a velocity of $12\,{\rm m/s}$ for $5\,{\rm s}$ and then continues in the same direction with $20\,{\rm m/s}$ for $3\,{\rm s}$. What is its average speed? Solution: Average velocity is displacement divided by elapsed time, i.e., $\bar{v}\equiv \frac{\Delta x_{tot}}{\Delta t_{tot}}$. Here, the object goes through two stages with two different displacements, so add them to find the total displacement. Thus,\[\bar{v}=\frac{x_1 + x_2}{t_1 +t_2}\] Again, to find the displacement, we use the same equation as the average velocity formula, i.e., $x=vt$. Thus, displacements are obtained as $x_1=v_1\,t_1=12\times 5=60\,{\rm m}$ and $x_2=v_2\,t_2=20\times 3=60\,{\rm m}$. Therefore, we have \begin{align*} \bar{v}&=\frac{x_1+x_2}{t_1+t_2}\\ \\&=\frac{60+60}{5+3}\\ \\&=\boxed{15\,{\rm m/s}}\end{align*} Problem (6): A plane flies the distance between two cities in $1$ hour and $30$ minutes with a velocity of $900\,{\rm km/h}$. Another plane covers that distance at $600\,{\rm km/h}$. What is the flight time of the second plane? Solution: first find the distance between two cities using the average velocity formula $\bar{v}=\frac{\Delta x}{\Delta t}$ as below \begin{align*} x&=vt\\&=900\times 1.5\\&=1350\,{\rm km}\end{align*} where we wrote one hour and a half minutes as $1.5\,\rm h$. Now use again the same kinematic equation above to find the time required for another plane \begin{align*} t&=\frac xv\\ \\ &=\frac{1350\,\rm km}{600\,\rm km/h}\\ \\&=2.25\,{\rm h}\end{align*} Thus, the time for the second plane is $2$ hours and $0.25$ of an hour, which converts to minutes as $2$ hours and ($0.25\times 60=15$) minutes. Problem (7): To reach a park located south of his jogging path, Henry runs along a 15-kilometer route. If he completes the journey in 1.5 hours, determine his speed and velocity. Solution: Henry travels his route to the park without changing direction along a straight line. Therefore, the total distance traveled in one direction equals the displacement, i.e, \[\text{distance traveled}=\Delta x=15\,\rm km\]Velocity is displacement divided by the time of travel \begin{align*} \text{velocity}&=\frac{\text{displacement}}{\text{time of travel}} \\\\ &=\frac{15\,\rm km}{1.5\,\rm h} \\\\ &=\boxed{10\,\rm km/h}\end{align*} and by definition, its average speed is \begin{align*} \text{speed}&=\frac{\text{distance covered}}{\text{time interval}}\\\\&=\frac{15\,\rm km}{1.5\,\rm h}\\\\&=\boxed{10\,\rm km/h}\end{align*} Thus, Henry's velocity is $10\,\rm km/h$ to the south, and its speed is $10\,\rm km/h$. As you can see, speed is simply a positive number, with units but velocity specifies the direction in which the object is moving. Problem (8): In 15 seconds, a football player covers the distance from his team's goal line to the opposing team's goal line and back to the midway point of the field having 100-yard-length. Find, (a) his average speed, and (b) the magnitude of the average velocity. Solution: The total length of the football field is $100$ yards or in meters, $L=91.44\,\rm m$. Going from one goal's line to the other and back to the midpoint of the field takes $15\,\rm s$ and covers a distance of $D=100+50=150\,\rm yd$.  Distance divided by the time of travel gets the average speed, \[\text{speed}=\frac{150\times 0.91}{15}=9.1\,\rm m/s\] To find the average velocity, we must find the displacement of the player between the initial and final points. The initial point is her own goal line and her final position is the midpoint of the field, so she has displaced a distance of $\Delta x=50\,\rm yd$ or $\Delta x=50\times 0.91=45.5\,\rm m$. Therefore, her velocity is calculated as follows \begin{align*} \text{velocity}&=\frac{\text{displacement}}{\text{time elapsed}} \\\\ &=\frac{45.5\,\rm m}{15\,\rm s} \\\\&=\boxed{3.03\quad \rm m/s}\end{align*} Contrary to the previous problem, here the motion is not in one direction, hence, the displacement is not equal to the distance traveled. Accordingly, the average speed is not equal to the magnitude of the average velocity. Problem (9): You begin at a pillar and run towards the east (the positive $x$ direction) for $250\,\rm m$ at an average speed of $5\,\rm m/s$. After that, you run towards the west for $300\,\rm m$ at an average speed of $4\,\rm m/s$ until you reach a post. Calculate (a) your average speed from pillar to post, and (b) your average velocity from pillar to post. Solution : First, you traveled a distance of $L_1=250\,\rm m$ toward east (or $+x$ direction) at $5\,\rm m/s$. Time of travel in this route is obtained as follows \begin{align*} t_1&=\frac{L_1}{v_1}\\\\ &=\frac{250}{5}\\\\&=50\,\rm s\end{align*} Likewise, traveling a distance of $L_2=300\,\rm m$ at $v_2=4\,\rm m/s$ takes \[t_2=\frac{300}{4}=75\,\rm s\] (a) Average speed is defined as the distance traveled (or path length) divided by the total time of travel \begin{align*} v&=\frac{\text{path length}}{\text{time of travel}} \\\\ &=\frac{L_1+L_2}{t_1+t_2}\\\\&=\frac{250+300}{50+75} \\\\&=4.4\,\rm m/s\end{align*} Therefore, you travel between these two pillars in $125\,\rm s$ and with an average speed of $4.4\,\rm m/s$. (b) Average velocity requires finding the displacement between those two points. In the first case, you move $250\,\rm m$ toward $+x$ direction, i.e., $L_1=+250\,\rm m$. Similarly, on the way back, you move $300\,\rm m$ toward the west ($-x$ direction) or $L_2=-300\,\rm m$. Adding these two gives us the total displacement between the initial point and the final point, \begin{align*} L&=L_1+L_2 \\\\&=(+250)+(-300) \\\\ &=-50\,\rm m\end{align*} The minus sign indicates that you are generally displaced toward the west. Finally, the average velocity is obtained as follows: \begin{align*} \text{average velocity}&=\frac{\text{displacement}}{\text{time of travel}} \\\\ &=\frac{-50}{125} \\\\&=-0.4\,\rm m/s\end{align*} A negative average velocity indicating motion to the left along the $x$-axis. This speed problem better makes it clear to us the difference between average speed and average speed. Unlike average speed, which is always a positive number, the average velocity in a straight line can be either positive or negative. Problem (10): What is the average speed for the round trip of a car moving uphill at 40 km/h and then back downhill at 60 km/h? Solution : Assuming the length of the hill to be $L$, the total distance traveled during this round trip is $2L$ since $L_{up}=L_{down}=L$. However, the time taken for going uphill and downhill was not provided. We can write them in terms of the hill's length $L$ as $t=\frac L v$. Applying the definition of average speed gives us \begin{align*} v&=\frac{\text{distance traveled}}{\text{total time}} \\\\ &=\frac{L_{up}+L_{down}}{t_{up}+t_{down}} \\\\ &=\cfrac{2L}{\cfrac{L}{v_{up}}+\cfrac{L}{v_{down}}} \end{align*} By reorganizing this expression, we obtain a formula that is useful for solving similar problems in the AP Physics 1 exams. \[\text{average speed}=\frac{2v_{up} \times v_{down}}{v_{up}+v_{down}}\] Substituting the numerical values into this, yields \begin{align*} v&=\frac{2(40\times 60)}{40+60} \\\\ &=\boxed{48\,\rm m/s}\end{align*} What if we were asked for the average velocity instead? During this round trip, the car returns to its original position, and thus its displacement, which defines the average velocity, is zero. Therefore, \[\text{average velocity}=0\,\rm m/s\] Acceleration ProblemsProblem (9): A car moves from rest to a speed of $45\,\rm m/s$ in a time interval of $15\,\rm s$. At what rate does the car accelerate? Solution : The car is initially at rest, $v_1=0$, and finally reaches $v_2=45\,\rm m/s$ in a time interval $\Delta t=15\,\rm s$. Average acceleration is the change in velocity, $\Delta v=v_2-v_1$, divided by the elapsed time $\Delta t$, so \[\bar{a}=\frac{45-0}{15}=\boxed{3\,\rm m/s^2} \] Problem (10): A car moving at a velocity of $15\,{\rm m/s}$, uniformly slows down. It comes to a complete stop in $10\,{\rm s}$. What is its acceleration? Solution: Let the car's uniform velocity be $v_1$ and its final velocity $v_2=0$. Average acceleration is the difference in velocities divided by the time taken, so we have: \begin{align*}\bar{a}&=\frac{\Delta v}{\Delta t}\\\\&=\frac{v_2-v_1}{\Delta t}\\\\&=\frac{0-15}{10}\\\\ &=\boxed{-1.5\,{\rm m/s^2}}\end{align*}The minus sign indicates the direction of the acceleration vector, which is toward the $-x$ direction. Problem (11): A car moves from rest to a speed of $72\,{\rm km/h}$ in $4\,{\rm s}$. Find the acceleration of the car. Solution: Known: $v_1=0$, $v_2=72\,{\rm km/h}$, $\Delta t=4\,{\rm s}$. Average acceleration is defined as the difference in velocities divided by the time interval between those points \begin{align*}\bar{a}&=\frac{v_2-v_1}{t_2-t_1}\\\\&=\frac{20-0}{4}\\\\&=5\,{\rm m/s^2}\end{align*} In above, we converted $\rm km/h$ to the SI unit of velocity ($\rm m/s$) as \[1\,\frac{km}{h}=\frac {1000\,m}{3600\,s}=\frac{10}{36}\, \rm m/s\] so we get \[72\,\rm km/h=72\times \frac{10}{36}=20\,\rm m/s\] Problem (12): A race car accelerates from an initial velocity of $v_i=10\,{\rm m/s}$ to a final velocity of $v_f = 30\,{\rm m/s}$ in a time interval of $2\,{\rm s}$. Determine its average acceleration. Solution: A change in the velocity of an object $\Delta v$ over a time interval $\Delta t$ is defined as an average acceleration. Known: $v_i=10\,{\rm m/s}$, $v_f = 30\,{\rm m/s}$, $\Delta t=2\,{\rm s}$. Applying definition of average acceleration, we get \begin{align*}\bar{a}&=\frac{v_f-v_i}{\Delta t}\\&=\frac{30-10}{2}\\&=10\,{\rm m/s^2}\end{align*} Problem (13): A motorcycle starts its trip along a straight line with a velocity of $10\,{\rm m/s}$ and ends with $20\,{\rm m/s}$ in the opposite direction in a time interval of $2\,{\rm s}$. What is the average acceleration of the car? Solution: Known: $v_i=10\,{\rm m/s}$, $v_f=-20\,{\rm m/s}$, $\Delta t=2\,{\rm s}$, $\bar{a}=?$. Using average acceleration definition we have \begin{align*}\bar{a}&=\frac{v_f-v_i}{\Delta t}\\\\&=\frac{(-20)-10}{2}\\\\ &=\boxed{-15\,{\rm m/s^2}}\end{align*}Recall that in the definition above, velocities are vector quantities. The final velocity is in the opposite direction from the initial velocity so a negative must be included. Problem (14): A ball is thrown vertically up into the air by a boy. After $4$ seconds, it reaches the highest point of its path. How fast does the ball leave the boy's hand? Solution : At the highest point, the ball has zero speed, $v_2=0$. It takes the ball $4\,\rm s$ to reach that point. In this problem, our unknown is the initial speed of the ball, $v_1=?$. Here, the ball accelerates at a constant rate of $g=-9.8\,\rm m/s^2$ in the presence of gravity. When the ball is tossed upward, the only external force that acts on it is the gravity force. Using the average acceleration formula $\bar{a}=\frac{\Delta v}{\Delta t}$ and substituting the numerical values into this, we will have \begin{gather*} \bar{a}=\frac{\Delta v}{\Delta t} \\\\ -9.8=\frac{0-v_1}{4} \\\\ \Rightarrow \boxed{v_1=39.2\,\rm m/s} \end{gather*} Note that $\Delta v=v_2-v_1$. Problem (15): A child drops crumpled paper from a window. The paper hit the ground in $3\,\rm s$. What is the velocity of the crumpled paper just before it strikes the ground? Solution : The crumpled paper is initially in the child's hand, so $v_1=0$. Let its speed just before striking be $v_2$. In this case, we have an object accelerating down in the presence of gravitational force at a constant rate of $g=-9.8\,\rm m/s^2$. Using the definition of average acceleration, we can find $v_2$ as below \begin{gather*} \bar{a}=\frac{\Delta v}{\Delta t} \\\\ -9.8=\frac{v_2-0}{3} \\\\ \Rightarrow v_2=3\times (-9.8)=\boxed{-29.4\,\rm m/s} \end{gather*} The negative shows us that the velocity must be downward, as expected! Problem (16): A car travels along the $x$-axis for $4\,{\rm s}$ at an average velocity of $10\,{\rm m/s}$ and $2\,{\rm s}$ with an average velocity of $30\,{\rm m/s}$ and finally $4\,{\rm s}$ with an average velocity $25\,{\rm m/s}$. What is its average velocity across the whole path? Solution: There are three different parts with different average velocities. Assume each trip is done in one dimension without changing direction. Thus, displacements associated with each segment are the same as the distance traveled in that direction and is calculated as below: \begin{align*}\Delta x_1&=v_1\,\Delta t_1\\&=10\times 4=40\,{\rm m}\\ \\ \Delta x_2&=v_2\,\Delta t_2\\&=30\times 2=60\,{\rm m}\\ \\ \Delta x_3&=v_3\,\Delta t_3\\&=25\times 4=100\,{\rm m}\end{align*}Now use the definition of average velocity, $\bar{v}=\frac{\Delta x_{tot}}{\Delta t_{tot}}$, to find it over the whole path\begin{align*}\bar{v}&=\frac{\Delta x_{tot}}{\Delta t_{tot}}\\ \\&=\frac{\Delta x_1+\Delta x_2+\Delta x_3}{\Delta t_1+\Delta t_2+\Delta t_3}\\ \\&=\frac{40+60+100}{4+2+4}\\ \\ &=\boxed{20\,{\rm m/s}}\end{align*} Problem (17): An object moving along a straight-line path. It travels with an average velocity $2\,{\rm m/s}$ for $20\,{\rm s}$ and $12\,{\rm m/s}$ for $t$ seconds. If the total average velocity across the whole path is $10\,{\rm m/s}$, then find the unknown time $t$. Solution: In this velocity problem, the whole path $\Delta x$ is divided into two parts $\Delta x_1$ and $\Delta x_2$ with different average velocities and times elapsed, so the total average velocity across the whole path is obtained as \begin{align*}\bar{v}&=\frac{\Delta x}{\Delta t}\\\\&=\frac{\Delta x_1+\Delta x_2}{\Delta t_1+\Delta t_2}\\\\&=\frac{\bar{v}_1\,t_1+\bar{v}_2\,t_2}{t_1+t_2}\\\\10&=\frac{2\times 20+12\times t}{20+t}\\\Rightarrow t&=80\,{\rm s}\end{align*} Note : whenever a moving object, covers distances $x_1,x_2,x_3,\cdots$ in $t_1,t_2,t_3,\cdots$ with constant or average velocities $v_1,v_2,v_3,\cdots$ along a straight-line without changing its direction, then its total average velocity across the whole path is obtained by one of the following formulas
Problem (18): A car travels one-fourth of its path with a constant velocity of $10\,{\rm m/s}$, and the remaining with a constant velocity of $v_2$. If the total average velocity across the whole path is $16\,{\rm m/s}$, then find the $v_2$? Solution: This is the third case of the preceding note. Let the length of the path be $L$ so \begin{align*}\bar{v}&=\frac{x_1+x_2}{\frac{x_1}{v_1}+\frac{x_2}{v_2}}\\\\16&=\frac{\frac 14\,L+\frac 34\,L}{\frac{\frac 14\,L}{10}+\frac{\frac 34\,L}{v_2}}\\\\\Rightarrow v_2&=20\,{\rm m/s}\end{align*} Problem (19): An object moves along a straight-line path. It travels for $t_1$ seconds with an average velocity $50\,{\rm m/s}$ and $t_2$ seconds with a constant velocity of $25\,{\rm m/s}$. If the total average velocity across the whole path is $30\,{\rm m/s}$, then find the ratio $\frac{t_2}{t_1}$? Solution: the velocities and times are known, so we have \begin{align*}\bar{v}&=\frac{v_1\,t_1+v_2\,t_2}{t_1+t_2}\\\\30&=\frac{50\,t_1+25\,t_2}{t_1+t_2}\\\\ \Rightarrow \frac{t_2}{t_1}&=4\end{align*} Read more related articles: Kinematics Equations: Problems and Solutions Position vs. Time Graphs Velocity vs. Time Graphs In the following section, some sample AP Physics 1 problems on acceleration are provided. Problem (20): An object moves with constant acceleration along a straight line. If its velocity at instant of $t_1 = 3\,{\rm s}$ is $10\,{\rm m/s}$ and at the moment of $t_2 = 8\,{\rm s}$ is $20\,{\rm m/s}$, then what is its initial speed? Solution: Let the initial speed at time $t=0$ be $v_0$. Now apply average acceleration definition in the time intervals $[t_0,t_1]$ and $[t_0,t_2]$ and equate them.\begin{align*}\text{average acceleration}\ \bar{a}&=\frac{\Delta v}{\Delta t}\\\\\frac{v_1 - v_0}{t_1-t_0}&=\frac{v_2-v_0}{t_2-t_0}\\\\ \frac{10-v_0}{3-0}&=\frac{20-v_0}{8-0}\\\\ \Rightarrow v_0 &=4\,{\rm m/s}\end{align*} In the above, $v_1$ and $v_2$ are the velocities at moments $t_1$ and $t_2$, respectively. Problem (21): For $10\,{\rm s}$, the velocity of a car that travels with a constant acceleration, changes from $10\,{\rm m/s}$ to $30\,{\rm m/s}$. How far does the car travel? Solution: Known: $\Delta t=10\,{\rm s}$, $v_1=10\,{\rm m/s}$ and $v_2=30\,{\rm m/s}$. Method (I) Without computing the acceleration: Recall that in the case of constant acceleration, we have the following kinematic equations for average velocity and displacement:\begin{align*}\text{average velocity}:\,\bar{v}&=\frac{v_1+v_2}{2}\\\text{displacement}:\,\Delta x&=\frac{v_1+v_2}{2}\times \Delta t\\\end{align*}where $v_1$ and $v_2$ are the velocities in a given time interval. Now we have \begin{align*} \Delta x&=\frac{v_1+v_2}{2}\\&=\frac{10+30}{2}\times 10\\&=200\,{\rm m}\end{align*} Method (II) with computing acceleration: Using the definition of average acceleration, first determine it as below \begin{align*}\bar{a}&=\frac{\Delta v}{\Delta t}\\\\&=\frac{30-10}{10}\\\\&=2\,{\rm m/s^2}\end{align*} Since the velocities at the initial and final points of the problem are given so use the below time-independent kinematic equation to find the required displacement \begin{align*} v_2^{2}-v_1^{2}&=2\,a\Delta x\\\\ (30)^{2}-(10)^{2}&=2(2)\,\Delta x\\\\ \Rightarrow \Delta x&=\boxed{200\,{\rm m}}\end{align*} Problem (22): A car travels along a straight line with uniform acceleration. If its velocity at the instant of $t_1=2\,{\rm s}$ is $36\,{\rm km/s}$ and at the moment $t_2=6\,{\rm s}$ is $72\,{\rm km/h}$, then find its initial velocity (at $t_0=0$)? Solution: Use the equality of definition of average acceleration $a=\frac{v_f-v_i}{t_f-t_i}$ in the time intervals $[t_0,t_1]$ and $[t_0,t_2]$ to find the initial velocity as below \begin{align*}\frac{v_2-v_0}{t_2-t_0}&=\frac{v_1-v_0}{t_1-t_0}\\\\ \frac{20-v_0}{6-0}&=\frac{10-v_0}{2-0}\\\\ \Rightarrow v_0&=\boxed{5\,{\rm m/s}}\end{align*} All these kinematic problems on speed, velocity, and acceleration are easily solved by choosing an appropriate kinematic equation. Keep in mind that these motion problems in one dimension are of the uniform or constant acceleration type. Projectiles are also another type of motion in two dimensions with constant acceleration. Author: Dr. Ali Nemati Date Published: 9/6/2020 Updated: Jun 28, 2023 © 2015 All rights reserved. by Physexams.com  2.2 Speed and VelocitySection learning objectives. By the end of this section, you will be able to do the following:
Teacher SupportThe learning objectives in this section will help your students master the following standards:
In addition, the High School Physics Laboratory Manual addresses content in this section in the lab titled: Position and Speed of an Object, as well as the following standards: Section Key Terms
In this section, students will apply what they have learned about distance and displacement to the concepts of speed and velocity. [BL] [OL] Before students read the section, ask them to give examples of ways they have heard the word speed used. Then ask them if they have heard the word velocity used. Explain that these words are often used interchangeably in everyday life, but their scientific definitions are different. Tell students that they will learn about these differences as they read the section. [AL] Explain to students that velocity, like displacement, is a vector quantity. Ask them to speculate about ways that speed is different from velocity. After they share their ideas, follow up with questions that deepen their thought process, such as: Why do you think that? What is an example? How might apply these terms to motion that you see every day? There is more to motion than distance and displacement. Questions such as, “How long does a foot race take?” and “What was the runner’s speed?” cannot be answered without an understanding of other concepts. In this section we will look at time , speed, and velocity to expand our understanding of motion. A description of how fast or slow an object moves is its speed. Speed is the rate at which an object changes its location. Like distance, speed is a scalar because it has a magnitude but not a direction. Because speed is a rate, it depends on the time interval of motion. You can calculate the elapsed time or the change in time, Δ t Δ t , of motion as the difference between the ending time and the beginning time The SI unit of time is the second (s), and the SI unit of speed is meters per second (m/s), but sometimes kilometers per hour (km/h), miles per hour (mph) or other units of speed are used. When you describe an object's speed, you often describe the average over a time period. Average speed , v avg , is the distance traveled divided by the time during which the motion occurs. You can, of course, rearrange the equation to solve for either distance or time Suppose, for example, a car travels 150 kilometers in 3.2 hours. Its average speed for the trip is A car's speed would likely increase and decrease many times over a 3.2 hour trip. Its speed at a specific instant in time, however, is its instantaneous speed . A car's speedometer describes its instantaneous speed. [OL] [AL] Caution students that average speed is not always the average of an object's initial and final speeds. For example, suppose a car travels a distance of 100 km. The first 50 km it travels 30 km/h and the second 50 km it travels at 60 km/h. Its average speed would be distance /(time interval) = (100 km)/[(50 km)/(30 km/h) + (50 km)/(60 km/h)] = 40 km/h. If the car had spent equal times at 30 km and 60 km rather than equal distances at these speeds, its average speed would have been 45 km/h. [BL] [OL] Caution students that the terms speed, average speed, and instantaneous speed are all often referred to simply as speed in everyday language. Emphasize the importance in science to use correct terminology to avoid confusion and to properly communicate ideas. Worked ExampleCalculating average speed. A marble rolls 5.2 m in 1.8 s. What was the marble's average speed? We know the distance the marble travels, 5.2 m, and the time interval, 1.8 s. We can use these values in the average speed equation. Average speed is a scalar, so we do not include direction in the answer. We can check the reasonableness of the answer by estimating: 5 meters divided by 2 seconds is 2.5 m/s. Since 2.5 m/s is close to 2.9 m/s, the answer is reasonable. This is about the speed of a brisk walk, so it also makes sense. Practice ProblemsA pitcher throws a baseball from the pitcher’s mound to home plate in 0.46 s. The distance is 18.4 m. What was the average speed of the baseball? The vector version of speed is velocity. Velocity describes the speed and direction of an object. As with speed, it is useful to describe either the average velocity over a time period or the velocity at a specific moment. Average velocity is displacement divided by the time over which the displacement occurs. Velocity, like speed, has SI units of meters per second (m/s), but because it is a vector, you must also include a direction. Furthermore, the variable v for velocity is bold because it is a vector, which is in contrast to the variable v for speed which is italicized because it is a scalar quantity. Tips For SuccessIt is important to keep in mind that the average speed is not the same thing as the average velocity without its direction. Like we saw with displacement and distance in the last section, changes in direction over a time interval have a bigger effect on speed and velocity. Suppose a passenger moved toward the back of a plane with an average velocity of –4 m/s. We cannot tell from the average velocity whether the passenger stopped momentarily or backed up before he got to the back of the plane. To get more details, we must consider smaller segments of the trip over smaller time intervals such as those shown in Figure 2.9 . If you consider infinitesimally small intervals, you can define instantaneous velocity , which is the velocity at a specific instant in time. Instantaneous velocity and average velocity are the same if the velocity is constant. Earlier, you have read that distance traveled can be different than the magnitude of displacement. In the same way, speed can be different than the magnitude of velocity. For example, you drive to a store and return home in half an hour. If your car’s odometer shows the total distance traveled was 6 km, then your average speed was 12 km/h. Your average velocity, however, was zero because your displacement for the round trip is zero. Watch PhysicsCalculating average velocity or speed. This video reviews vectors and scalars and describes how to calculate average velocity and average speed when you know displacement and change in time. The video also reviews how to convert km/h to m/s.
This video does a good job of reinforcing the difference between vectors and scalars. The student is introduced to the idea of using ‘s’ to denote displacement, which you may or may not wish to encourage. Before students watch the video, point out that the instructor uses s → s → for displacement instead of d, as used in this text. Explain the use of small arrows over variables is a common way to denote vectors in higher-level physics courses. Caution students that the customary abbreviations for hour and seconds are not used in this video. Remind students that in their own work they should use the abbreviations h for hour and s for seconds. Calculating Average VelocityA student has a displacement of 304 m north in 180 s. What was the student's average velocity? We know that the displacement is 304 m north and the time is 180 s. We can use the formula for average velocity to solve the problem. Since average velocity is a vector quantity, you must include direction as well as magnitude in the answer. Notice, however, that the direction can be omitted until the end to avoid cluttering the problem. Pay attention to the significant figures in the problem. The distance 304 m has three significant figures, but the time interval 180 s has only two, so the quotient should have only two significant figures. Note the way scalars and vectors are represented. In this book d represents distance and displacement. Similarly, v represents speed, and v represents velocity. A variable that is not bold indicates a scalar quantity, and a bold variable indicates a vector quantity. Vectors are sometimes represented by small arrows above the variable. Use this problem to emphasize the importance of using the correct number of significant figures in calculations. Some students have a tendency to include many digits in their final calculations. They incorrectly believe they are improving the accuracy of their answer by writing many of the digits shown on the calculator. Point out that doing this introduces errors into the calculations. In more complicated calculations, these errors can propagate and cause the final answer to be wrong. Instead, remind students to always carry one or two extra digits in intermediate calculations and to round the final answer to the correct number of significant figures. Solving for Displacement when Average Velocity and Time are KnownLayla jogs with an average velocity of 2.4 m/s east. What is her displacement after 46 seconds? We know that Layla's average velocity is 2.4 m/s east, and the time interval is 46 seconds. We can rearrange the average velocity formula to solve for the displacement. The answer is about 110 m east, which is a reasonable displacement for slightly less than a minute of jogging. A calculator shows the answer as 110.4 m. We chose to write the answer using scientific notation because we wanted to make it clear that we only used two significant figures. Dimensional analysis is a good way to determine whether you solved a problem correctly. Write the calculation using only units to be sure they match on opposite sides of the equal mark. In the worked example, you have m = (m/s)(s). Since seconds is in the denominator for the average velocity and in the numerator for the time, the unit cancels out leaving only m and, of course, m = m. Solving for Time when Displacement and Average Velocity are KnownPhillip walks along a straight path from his house to his school. How long will it take him to get to school if he walks 428 m west with an average velocity of 1.7 m/s west? We know that Phillip's displacement is 428 m west, and his average velocity is 1.7 m/s west. We can calculate the time required for the trip by rearranging the average velocity equation. Here again we had to use scientific notation because the answer could only have two significant figures. Since time is a scalar, the answer includes only a magnitude and not a direction.
A bird flies with an average velocity of 7.5 m/s east from one branch to another in 2.4 s. It then pauses before flying with an average velocity of 6.8 m/s east for 3.5 s to another branch. What is the bird’s total displacement from its starting point? Virtual PhysicsThe walking man. In this simulation you will put your cursor on the man and move him first in one direction and then in the opposite direction. Keep the Introduction tab active. You can use the Charts tab after you learn about graphing motion later in this chapter. Carefully watch the sign of the numbers in the position and velocity boxes. Ignore the acceleration box for now. See if you can make the man’s position positive while the velocity is negative. Then see if you can do the opposite. Grasp CheckWhich situation correctly describes when the moving man’s position was negative but his velocity was positive?
This is a powerful interactive animation, and it can be used for many lessons. At this point it can be used to show that displacement can be either positive or negative. It can also show that when displacement is negative, velocity can be either positive or negative. Later it can be used to show that velocity and acceleration can have different signs. It is strongly suggested that you keep students on the Introduction tab. The Charts tab can be used after students learn about graphing motion later in this chapter. Check Your Understanding
If you divide the total distance traveled on a car trip (as determined by the odometer) by the time for the trip, are you calculating the average speed or the magnitude of the average velocity, and under what circumstances are these two quantities the same?
Use the Check Your Understanding questions to assess students’ achievement of the sections learning objectives. If students are struggling with a specific objective, the Check Your Understanding will help identify which and direct students to the relevant content. Assessment items in TUTOR will allow you to reassess. As an Amazon Associate we earn from qualifying purchases. This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission. Want to cite, share, or modify this book? This book uses the Creative Commons Attribution License and you must attribute Texas Education Agency (TEA). The original material is available at: https://www.texasgateway.org/book/tea-physics . Changes were made to the original material, including updates to art, structure, and other content updates. Access for free at https://openstax.org/books/physics/pages/1-introduction
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 Real World Algebra by Edward ZaccaroAlgebra is often taught abstractly with little or no emphasis on what algebra is or how it can be used to solve real problems. Just as English can be translated into other languages, word problems can be "translated" into the math language of algebra and easily solved. Real World Algebra explains this process in an easy to understand format using cartoons and drawings. This makes self-learning easy for both the student and any teacher who never did quite understand algebra. Includes chapters on algebra and money, algebra and geometry, algebra and physics, algebra and levers and many more. Designed for children in grades 4-9 with higher math ability and interest but could be used by older students and adults as well. Contains 22 chapters with instruction and problems at three levels of difficulty. One to one maths interventions built for KS4 success Weekly online one to one GCSE maths revision lessons now available In order to access this I need to be confident with: Multiplication and division Converting units of length (distance) Rearranging the subject of a formula Substitution into formulae This topic is relevant for:  Speed Distance Time Speed Distance Time TriangleHere we will learn about the speed distance time triangle including how they relate to each other, how to calculate each one and how to solve problems involving them. There are also speed distance time triangle worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck. What is speed distance time?Speed distance time is the formula used to explain the relationship between speed, distance and time. That is speed = distance ÷ time . Or to put it another way distance divided by speed will give you the time. Provided you know two of the inputs you can work out the third. For example if a car travels for 2 hours and covers 120 miles we can work out speed as 120 ÷ 2 = 60 miles per hour. The units of the the distance and time tell you the units for the speed. What is the speed distance time triangle?The speed distance time triangle is a way to describe the relationship between speed, distance and time as shown by the formula below. \textbf{Speed } \bf{=} \textbf{ distance } \bf{\div} \textbf{ time} “Speed equals distance divided by time” Let’s look at an example to calculate speed. If a car travels 66km in 1.5 hours then we can use this formula to calculate the speed. This formula can also be rearranged to calculate distance or calculate time given the other two measures. An easy way to remember the formula and the different rearrangements is to use this speed distance time triangle.  From this triangle we can work out how to calculate each measure: We can ‘cover up’ what we are trying to find and the formula triangle tells us what calculation to do.  Let’s look at an example to calculate time. How long does it take for a car to travel 34 miles at a speed of 68 miles per hour? Let’s look at an example to calculate distance. What distance does a bike cover if it travels at a speed of 7 metres per second for 50 seconds?  What is the speed distance time formula?The speed distance time formula is just another way of referring to the speed distance time triangle or calculation you can use to determine speed, time or distance.
Time problemWe can solve problems involving time by remembering the formula for speed , distance and time .  Calculate the time if a car travels at 15 miles at a speed of 36 mph. Time = distance ÷ speed Time = 15 ÷ 36 = 0.42 hours 0.42 ✕ 60 = 25.2 minutes A train travels 42km between two stops at an average speed of 36 km/h. If the train departs at 4 pm, when does the train arrive? Time = 42 ÷ 36 = 1.17 hours 1.17 ✕ 60= 70 minutes = 1 hour 10 minutes. The average speed of a scooter is 18 km/h and the average speed of a cycle is 10 km/h. When both have travelled 99 km what is the difference in the time taken? Time A = 99 ÷ 18 = 5.5 hours Time B= 99 ÷ 10 = 9.9 hours Difference in time = 9.9 – 5.5 = 4.4 hours 4.4 hours = 4 hours and 24 minutes Units of speed, distance and time
The average speed of a small plane is 124mph. The average walking speed of a person is 1.4m/s.
The distance from London to Birmingham is 162.54km. 
The time taken for the Earth to orbit the sun is 1 year or 365 days. We don’t measure this in smaller units like minutes of hours. A short bus journey however, would be measured in minutes. Speed, distance and time are proportional.  If we know two of the measurements we can find the other. A car drives 150 miles in 3 hours. Calculate the average speed, in mph, of the car. Distance = 150 miles Time = 3 hours Speed = 150÷ 3= 50mph Speed, distance, time and units of measureIt is very important to be aware of the units being used when calculating speed, distance and time.
Note that speed is a compound measure and therefore involves two units; a combination of a distance in relation to a time. When you use the speed distance time formula you must check that each measure is in the appropriate unit before you carry out the calculation. Sometimes you will need to convert a measure into different units. Here are some useful conversions to remember. Units of length Units of time 1 minute = 60 seconds 1 hour = 60 minutes 1 day = 24 hours Let’s look at an example. What distance does a bike cover if it travels at a speed of 5 metres per second for 3 minutes? Note here that the speed involves seconds, but the time given is in minutes. So before using the formula you must change 3 minutes into seconds. 3 minutes = 3\times 60 =180 seconds Note also that sometimes you may need to convert an answer into different units at the end of a calculation. Constant speed / average speedFor the GCSE course you will be asked to calculate either a constant speed or an average speed . Both of these can be calculated using the same formula as shown above. However, this terminology is used because in real life speed varies throughout a journey. You should also be familiar with the terms acceleration (getting faster) and deceleration (getting slower). Constant speed A part of a journey where the speed stays the same. Average speed A journey might involve a variety of different constant speeds and some acceleration and deceleration. We can use the formula for speed to calculate the average speed over the course of the whole journey. Average Speed FormulaAverage speed is the total distance travelled by an object divided by the total time taken. To do this we can use the formula Average speed =\frac{Total\, distance}{Total\, time} If we are calculating an average speed in mph or km/h, we will need to ensure we have decimalised the time before we divide. How to calculate speed distance timeIn order to calculate speed, distance or time: Write down the values of the measures you know with the units.  Check that the units are compatible with each other, converting them if necessary. Substitute the values into the selected formula and carry out the resulting calculation. Write your final answer with the required units. Explain how to calculate speed distance time Speed distance time triangle worksheetGet your free speed distance time triangle worksheet of 20+ questions and answers. Includes reasoning and applied questions. Related lessons on compound measuresSpeed distance time is part of our series of lessons to support revision on compound measures . You may find it helpful to start with the main compound measures lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:
Speed distance time triangle examplesExample 1: calculating average speed. Calculate the average speed of a car which travels 68 miles in 2 hours. Speed: unknown Distance: 68 miles Time: 2 hours 2 Write down the formula you need to use from the speed, distance, time triangle.  3 Check that the units are compatible with each other, converting them if necessary. The distance is in miles and the time is in hours. These units are compatible to give the speed in miles per hour. 4 Substitute the values into the formula and carry out the resulting calculation. 5 Write your final answer with the required units. Example 2: calculating timeA golden eagle can fly at a speed of 55 kilometres per hour. Calculate the time taken for a golden eagle to fly 66 \ km, giving your answer in hours. Speed: 55 \ km/hour Distance: 66 \ km Time: unknown Write down the formula you need to use from the speed, distance, time triangle.  T=\frac{D}{S} Time = distance \div speed Speed is in km per hour and the distance is in km , so these are compatible to give an answer for time in hours. Example 3: calculating distanceCalculate the distance covered by a train travelling at a constant speed of 112 miles per hour for 4 hours. Speed: 112 \ mph Distance: unknown Time: 4 hours  D= S \times T Distance = speed \times time Speed is in miles per hour. The time is in hours. These units are compatible to find the distance in miles. Example 4: calculating speed with unit conversionA car travels for 1 hour and 45 minutes, covering a distance of 63 miles. Calculate the average speed of the car giving your answer in miles per hour (mph) . Distance: 63 miles Time: 1 hour and 45 minutes  S = \frac{D}{T} Speed = distance \div time The distance is in miles . The time is in hours and minutes. To calculate the speed in miles per hour , the time needs to be converted into hours only. 1 hour 45 minutes = 1\frac{3}{4} hours = 1.75 hours Example 5: calculating time with unit conversionA small plane can travel at an average speed of 120 miles per hour. Calculate the time taken for this plane to fly 80 miles giving your answer in minutes. Speed: 120 \ mph Distance: 80 \ miles  T = \frac{D}{S} Speed is in miles per hour and the distance is in miles . These units are compatible to find the time in hours. \frac{2}{3} hours in minutes \frac{2}{3} \times 60 = 40 Example 6: calculating distance with unit conversionA train travels at a constant speed of 96 miles per hour for 135 minutes. Calculate the distance covered giving your answer in miles. Speed: 96 \ mph Time: 135 minutes  D = S \times T The speed is in miles per hour , but the time is in minutes. To make these compatible the time needs changing into hours and then the calculation will give the distance in miles . 135 minutes 135 \div 60 = \frac{9}{4} = 2\frac{1}{4} = 2.25 Common misconceptions
Make sure you rearrange the formula correctly. One of the simplest ways of doing this is to use the formula triangle. In the triangle you cover up the measure you want to find out and then the triangle shows you what calculation to do with the other two measures. 
When using the speed distance time formula you must ensure that the units of the measures are compatible. For example, if a car travels at 80 \ km per hour for 30 minutes and you are asked to calculate the distance, a common error is to substitute the values straight into the formula and do the following calculation. Distance = speed \times time = 80 \times 30 = 2400 \ km The correct way is to notice that the speed uses hours but the time given is in minutes. Therefore you must change 30 minutes into 0.5 hours and substitute these compatible values into the formula and do the following calculation. Distance = speed \times time = 80 \times 0.5 = 40 \ km Practice speed distance time triangle questions1. A car drives 120 miles in 3 hours. Calculate its average speed.  2. A cyclist travels 100 miles at an average speed of 20 \ mph. Calculate how long the journey takes. 3. An eagle flies for 30 minutes at a speed of 66 \ km per hour. Calculate the total distance the bird has flown. 30 minutes = 0.5 hours 4. Calculate the average speed of a lorry travelling 54 miles in 90 minutes. Give your answer in miles per hour (mph). Firstly convert 90 minutes to hours. 90 minutes = 1.5 hours 5. Calculate the time taken for a plane to fly 90 miles at an average speed of 120 \ mph. Give your answer in minutes. 180 minutes Convert 0.75 hours to minutes 6. A helicopter flies 18 \ km in 20 minutes. Calculate its average speed in km/h . Firstly convert 20 minutes to hours. 20 minutes is a third of an hour or \frac{1}{3} hours. \begin{aligned} &Speed = distance \div time \\\\ &Speed =18 \div \frac{1}{3} \\\\ &Speed = 54 \\\\ &54 \ km/h \end{aligned} Speed distance time triangle GCSE questions1. A commercial aircraft travels from its origin to its destination in a time of 2 hours and 15 minutes. The journey is 1462.5 \ km. What is the average speed of the plane in km/hour? 2 hours 15 minutes = 2\frac{15}{60} = 2\frac{1}{4} = 2.25 2. John travelled 30 \ km in 90 minutes. Nadine travelled 52.5 \ km in 2.5 hours. Who had the greater average speed? You must show your working. 90 minutes = 1.5 hours John = 30 \div 1.5 = 20 \ km/h Nadine = 52.5 \div 2.5 = 21 \ km/h Nadine has the greater average speed. 3. The distance from Birmingham to Rugby is 40 miles. Omar drives from Rugby to Birmingham at 60 \ mph. Ayushi drives from Rugby to Birmingham at 50 \ mph. How much longer was Ayushi’s journey compared to Omar’s journey? Give your answer in minutes. For calculating time in hours for Omar or Ayushi. For converting hours into minutes for Omar or Ayushi. For correct final answer of 8 minutes. Learning checklistYou have now learned how to:
The next lessons are
Still stuck?Prepare your KS4 students for maths GCSEs success with Third Space Learning. Weekly online one to one GCSE maths revision lessons delivered by expert maths tutors.  Find out more about our GCSE maths tuition programme. Privacy OverviewSpeed FormulaThe speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance traveled by a body in a given period of time. The SI unit of speed is m/s. In this section, we will learn more about the speed formula and its applications. What is the Speed Formula?Let's move further and explore more about the speed formula in this section. Different units can be used to express speed, like m/s, km/hr, miles/hr, etc. The dimensional formula of speed is [LT -1 ]. Speed is a measure of how fast a body is moving. The formula for the speed of a given body can be expressed as, Formula for SpeedSpeed = Distance ÷ Time  How to Use Speed Formula?Speed formula can be used to find the speed of objects, given the distance and time taken to cover that distance. We can also use the speed formula to calculate the distance or time by substituting the known values in the formula for speed and further evaluating, Distance = Speed × Time or, Time = Distance/Speed Let's take a quick look at an example showing how to use the formula for speed. Example: What is your speed if you travel 3600 m in 30 minutes? Solution: Using Formula for Speed, Speed = Distance ÷ Time Speed = 3600 ÷ (30 × 60) = 2 Answer: Your speed if you travel 3600m in 30 minutes is 2 m/s.  Book a Free Trial Class Examples on Speed FormulaLet us solve some interesting problems using the speed formula. Example 1: A train covered a distance of 120 km in an hour. Determine the speed of the train in m/s using the speed formula. To find: The speed of the train. The distance covered by a train in meters = 120×1000m = 120000m Time taken by train in seconds = 60×60 = 3600 second Using Formula for Speed, Speed = Distance/Time = 120000/3600 = 33.3m/sec Answer: The speed of the train is 33.3 m/s. Example 2: A cyclist covers 20 km in 50 minutes. Use the speed formula to calculate the speed of the cyclist in m/s. Solution: To find: The speed of a cyclist. The distance covered by a cyclist in meters = 20×1000 =20000m Time taken by cyclist in seconds = 50×60= 3000 second Using formula for speed, Speed = Distance/Time = 20000/3000 = 6.67m/sec Answer: The speed of the cyclist is 6.67 m/s. Example 3: Using the speed formula calculate the speed of a person in kilometers per hour if the distance he travels is 40 kilometers in 2 hours? The formula for speed is [Speed = Distance ÷ Time] Distance = 40 kilometers Time = 2 hours Speed = (40 ÷ 2) km/hr = 20 kilometers per hour Answer: The speed of the person is 20 kilometers per hour. FAQs on Speed FormulaHow to calculate distance using speed formula . The formula for Speed is given as [Speed = Distance ÷ Time]. To calculate the distance, the speed formula can be molded as [Distance = Speed × Time]. How to Calculate Time Using Speed Formula?The formula for speed is given as [Speed = Distance ÷ Time].To calculate the time, the speed formula will be molded as [Time = Distance Travelled ÷ Speed]. How to Use the Formula for Speed?Speed formula can be used in our day-to-day lives to find the speed of objects. To understand how to use the formula for speed let us consider an example. Example: What is your speed if you travel 4000m in 40 minutes? Solution: Using Formula for Speed, Speed = Distance ÷ Time Speed = 4000 ÷ (40 × 60) = 1.67m/s. Answer: Your speed if you travel 4000m in 40 minutes is 1.67 m/s. What will be the General Speed Formula for an Object?The general speed formula for an object is given as [Speed = Distance ÷ Time]. SI units of speed is m/s. Speed Distance Time Videohttps://youtu.be/rQUwNC0gqdg?t=2557 Speed is the scalar quantity of change in distance travelled along a path, divided by the time it takes to travel that part of the path. Contrast with velocitySpeed is different from velocity, the latter has direction. Here's why that changes things: ![A\\\rule{0.513\textwidth}{1pt}\\[-1.5pt]\ignorespaces\rule{1pt}{1cm}\rule{1cm}{1pt}\rule{1pt}{1cm}\rule{1cm}{1pt}\rule{1pt}{1cm}\rule{1cm}{1pt}\rule{1pt}{1cm}\rule{1cm}{1pt}\rule{1pt}{1cm}\rule{1cm}{1pt}\rule{1pt}{1cm}\\\rule{0.513\textwidth}{0pt}B](https://latex.artofproblemsolving.com/f/b/2/fb23dca793414d31537f6da29c09761e00b9d866.png "problem solving in speed") On the other hand, velocity depends on a distance (called displacement) and ' direction . If A walks around the block (4 equal sides), she may have walked 4 units of length in 4 minutes; giving her a speed of 1 unit of length per minute. However she has a distance from point of origin (called displacement) of 0 units of length; therefore her velocity is 0 units of length per minute in the opposite path direction to which she arrived back at the point of origin. Something appears to not have loaded correctly. Click to refresh . Average Speed ProblemsRelated Pages Rate, Time, Distance Solving Speed, Time, Distance Problems Using Algebra More Algebra Lessons In these lessons, we will learn how to solve word problems involving average speed. There are three main types of average problems commonly encountered in school algebra: Average (Arithmetic Mean) Weighted Average and Average Speed. How to calculate Average Speed?The following diagram shows the formula for average speed. Scroll down the page for more examples and solutions on calculating the average speed.  Examples Of Average Speed ProblemsExample: John drove for 3 hours at a rate of 50 miles per hour and for 2 hours at 60 miles per hour. What was his average speed for the whole journey? Solution: Step 1: The formula for distance is Distance = Rate × Time Total distance = 50 × 3 + 60 × 2 = 270 Step 2: Total time = 3 + 2 = 5 Step 3: Using the formula: Answer: The average speed is 54 miles per hour. Be careful! You will get the wrong answer if you add the two speeds and divide the answer by two. How To Solve The Average Speed Problem?How to calculate the average speed? Example: The speed paradox: If I drive from Oxford to Cambridge at 40 miles per hour and then from Cambridge to Oxford at 60 miles per hour, what is my average speed for the whole journey? How To Find The Average Speed For A Round Trip?Example: On Alberto’s drive to his aunt’s house, the traffic was light, and he drove the 45-mile trip in one hour. However, the return trip took his two hours. What was his average trip for the round trip? How To Find The Average Speed Of An Airplane With Good And Bad Weather?Example: Mae took a non-stop flight to visit her grandmother. The 750-mile trip took three hours and 45 minutes. Because of the bad weather, the return trip took four hours and 45 minutes. What was her average speed for the round trip? How To Relate Speed To Distance And Time?If you are traveling in a car that travels 80km along a road in one hour, we say that you are traveling at an average of 80kn/h. Average speed is the total distance divided by the total time for the trip. Therefore, speed is distance divided by time. Instantaneous speed is the speed at which an object is traveling at any particular instant. If the instantaneous speed of a car remains the same over a period of time, then we say that the car is traveling with constant speed. The average speed of an object is the same as its instantaneous speed if that object is traveling at a constant speed. How To Calculate Average Speed In Word Problems?Example: Keri rollerblades to school, a total distance of 4.5km. She has to slow down twice to cross busy streets, but overall the journey takes her 0.65h. What is Keri’s average speed during the trip? How To Use Average Speed To Calculate The Distance Traveled?Example: Elle drives 169 miles from Sheffield to London. Her average speed is 65 mph. She leaves Sheffield at 6:30 a.m. Does she arrive in London by 9:00 a.m.? How To Use Average Speed To Calculate The Time Taken?Example: Marie Ann is trying to predict the time required to ride her bike to the nearby beach. She knows that the distance is 45 km and, from other trips, that she can usually average about 20 km/h. Predict how long the trip will take.  We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page. TIME SPEED AND DISTANCE PROBLEMSFormulas .  To know the shortcuts required to solve problems on time, speed and distance, please click here Problem 1 : If a person drives his car in the speed 50 miles per hour, how far can he cover in 2.5 hours? Given : Speed is 50 miles per hour. So, the distance covered in 1 hour is Then, the distance covered in 2.5 hours is = 2.5 ⋅ 50 miles = 125 miles So, the person can cover 125 miles of distance in 2.5 hours. Problem 2 : If a person travels at a speed of 40 miles per hour. At the same rate, how long will he take to cover 160 miles distance? Given : Speed is 40 miles per hour. The formula to find the time when distance and speed are given is Time taken to cover the distance of 160 miles is So, the person will take 4 hours to cover 160 miles distance at the rate of 40 miles per hour. Problem 3 : A person travels at a speed of 60 miles per hour. How far will he travel in 4.5 hours? Given : Speed is 60 miles per hour. The distance covered in 1 hour is Then, the distance covered in 4.5 hours is = 4.5 ⋅ 60 miles = 270 miles So, the person will travel 270 miles distance in 4.5 hours. Problem 4 : A person travels at a speed of 60 kms per hour. Then how many meters can he travel in 5 minutes? Given : Speed is 60 kms per hour. The distance covered in 1 hour or 60 minutes is = 60 ⋅ 1000 meters = 60000 meters Then the distance covered in 1 minute is The distance covered in 5 minutes is = 5 ⋅ 1000 = 5000 meters So, the person can cover 5000 meters distance in 5 minutes. Problem 5 : A person covers 108 kms in 3 hours. What is his speed in meter per second? Given : Distance is 108 kms and time is 3 hours. The given distance in meters : = 108 ⋅ 1000 = 108,000 meters The given time in seconds : = 3 ⋅ 60 minutes = 180 minutes = 180 ⋅ 60 seconds = 10,800 seconds The formula to find the speed is Speed in meter per second is = ¹⁰⁸⁰⁰⁰⁄₁₀₈₀₀ So, his speed in meter per second is 10. Problem 6 : A person covers 90 kms in 2 hours 30 minutes. Find the speed in meter per second. Given : Distance is 90 kms and time is 2 hrs 30 min. = 90 ⋅ 1000 = 90,000 meters = 2 hrs 30 min = (120 + 30) min = 150 minutes = 150 ⋅ 60 seconds = 9,000 seconds = ⁹⁰⁰⁰⁰⁄₉₀₀₀ Problem 7 : A person travels at the rate of 60 miles per hour and covers 300 miles in 5 hours. If he reduces his speed by 10 miles per hour, how long will he take to cover the same distance? Original speed is 60 miles per hour. If the speed is reduced by 10 miles per hour, then the new speed is = 50 miles per hour Distance to be covered is 300 miles. The formula to find time is Time taken to cover 300 miles distance at the speed of 50 miles per hour is So, if the person reduces his speed by 10 miles per hour, he will take 6 hours to cover 300 miles distance. Problem 8 : A person travels 50 kms per hour. If he increases his speed by 10 kms per hour, how many minutes will he take to cover 8000 meters? Original speed is 50 kms per hour. If the speed is increased by 10 kms per hour, then the new speed is = 60 kms per hour Because, we have to find the time in minutes for the distance given in meters, let us change the speed from kms per hour into meters per minute. 1 hour ----> 60 kms 1 ⋅ 60 minutes ----> 60 ⋅ 1000 meters 60 minutes ----> 60000 meters 1 minute ----> ⁶⁰⁰⁰⁰⁄₆₀ meters 1 minute ----> 1000 meters So, the speed is 1000 meters/minute. Time = Distance/Speed Time taken to cover 8000 meters distance at the speed of 1000 meters per minute is = ⁸⁰⁰⁰⁄₁₀₀₀ = 8 minutes So, if the person increases his speed by 10 kms per hour, he will take 8 minutes to cover 8000 meters distance. Problem 9 : A person can travel at the speed of 40 miles per hour. If the speed is increased by 50%, how long will it take to cover 330 miles? Original speed is 40 miles per hour. If the speed is increased by 50%, then the new speed is = 150% of 40 = 1.5 ⋅ 40 = 60 miles per hour Distance to be covered is 330 miles. Time taken to cover 330 miles distance at the speed of 60 miles per hour is = 5.5 hours = 5 hrs 30 minutes So, if the person is increased by 50%, it will take 5 hrs 30 minutes to cover 330 miles distance. Problem 10 : A person speed at a rate of 40 kms per hour. If he increases his speed by 20%, what is his new speed in meter per minute? Original speed is 40 kms per hour If the speed is increased by 20%, then the new speed is = 120 % of 40 = 1.2 ⋅ 40 = 48 kms per hour Now, let us change the speed from kms per hour into meters per minute. 1 hour ----> 48 kms 1 ⋅ 60 minutes ----> 48 ⋅ 1000 meters 60 minutes ----> 48,000 meters 1 minute ----> ⁴⁸⁰⁰⁰⁄₆₀ meters 1 minute ----> 800 meters So, the speed is 800 meters/minute. If the person increases his speed by 20%, his new speed will be 800 meter per minute. 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In math, distance, rate, and time are three important concepts you can use to solve many problems if you know the formula. Distance is the length of space traveled by a moving object or the length measured between two points. It is usually denoted by d in math problems . The rate is the speed at which an object or person travels. It is usually denoted by r in equations . Time is the measured or measurable period during which an action, process, or condition exists or continues. In distance, rate, and time problems, time is measured as the fraction in which a particular distance is traveled. Time is usually denoted by t in equations. Solving for Distance, Rate, or TimeWhen you are solving problems for distance, rate, and time, you will find it helpful to use diagrams or charts to organize the information and help you solve the problem. You will also apply the formula that solves distance, rate, and time, which is distance = rate x tim e. It is abbreviated as: There are many examples where you might use this formula in real life. For example, if you know the time and rate a person is traveling on a train, you can quickly calculate how far he traveled. And if you know the time and distance a passenger traveled on a plane, you could quickly figure the distance she traveled simply by reconfiguring the formula. Distance, Rate, and Time ExampleYou'll usually encounter a distance, rate, and time question as a word problem in mathematics. Once you read the problem, simply plug the numbers into the formula. For example, suppose a train leaves Deb's house and travels at 50 mph. Two hours later, another train leaves from Deb's house on the track beside or parallel to the first train but it travels at 100 mph. How far away from Deb's house will the faster train pass the other train? To solve the problem, remember that d represents the distance in miles from Deb's house and t represents the time that the slower train has been traveling. You may wish to draw a diagram to show what is happening. Organize the information you have in a chart format if you haven't solved these types of problems before. Remember the formula: distance = rate x time When identifying the parts of the word problem, distance is typically given in units of miles, meters, kilometers, or inches. Time is in units of seconds, minutes, hours, or years. Rate is distance per time, so its units could be mph, meters per second, or inches per year. Now you can solve the system of equations: 50t = 100(t - 2) (Multiply both values inside the parentheses by 100.) 50t = 100t - 200 200 = 50t (Divide 200 by 50 to solve for t.) t = 4 Substitute t = 4 into train No. 1 d = 50t = 50(4) = 200 Now you can write your statement. "The faster train will pass the slower train 200 miles from Deb's house." Sample ProblemsTry solving similar problems. Remember to use the formula that supports what you're looking for—distance, rate, or time. d = rt (multiply) r = d/t (divide) t = d/r (divide) Practice Question 1A train left Chicago and traveled toward Dallas. Five hours later another train left for Dallas traveling at 40 mph with a goal of catching up with the first train bound for Dallas. The second train finally caught up with the first train after traveling for three hours. How fast was the train that left first going? Remember to use a diagram to arrange your information. Then write two equations to solve your problem. Start with the second train, since you know the time and rate it traveled: Second train t x r = d 3 x 40 = 120 miles First train t x r = d 8 hours x r = 120 miles Divide each side by 8 hours to solve for r. 8 hours/8 hours x r = 120 miles/8 hours r = 15 mph Practice Question 2One train left the station and traveled toward its destination at 65 mph. Later, another train left the station traveling in the opposite direction of the first train at 75 mph. After the first train had traveled for 14 hours, it was 1,960 miles apart from the second train. How long did the second train travel? First, consider what you know: First train r = 65 mph, t = 14 hours, d = 65 x 14 miles Second train r = 75 mph, t = x hours, d = 75x miles Then use the d = rt formula as follows: d (of train 1) + d (of train 2) = 1,960 miles 75x + 910 = 1,960 75x = 1,050 x = 14 hours (the time the second train traveled)
Speed and VelocitySpeed is how fast something moves. Velocity is speed with a direction .  Saying Ariel the Dog runs at 9 km/h (kilometers per hour) is a speed. But saying he runs 9 km/h Westwards is a velocity.
Imagine something moving back and forth very fast: it has a high speed, but a low (or zero) velocity. Speed is measured as distance moved over time. Speed = Distance Time Example: A car travels 50 km in one hour.Its average speed is 50 km per hour (50 km/h) Speed = Distance Time = 50 km 1 hour We can also use these symbols: Speed = Δs Δt Where Δ (" Delta ") means "change in", and
 Example: You run 360 m in 60 seconds.So your speed is 6 meters per second (6 m/s). Speed is commonly measured in:
A km is 1000 m, and there are 3600 seconds in an hour, so we can convert like this (see Unit Conversion Method to learn more): So 1 m/s is equal to 3.6 km/h Example: What is 20 m/s in km/h ?20 m/s × 3.6 km/h 1 m/s = 72 km/h Example: What is 120 km/h in m/s ?120 km/h × 1 m/s 3.6 km/h = 33.333... m/s Average vs Instantaneous SpeedThe examples so far calculate average speed : how far something travels over a period of time. But speed can change as time goes by. A car can go faster and slower, maybe even stop at lights. So there is also instantaneous speed : the speed at an instant in time. We can try to measure it by using a very short span of time (the shorter the better). Example: Sam uses a stopwatch and measures 1.6 seconds as the car travels between two posts 20 m apart. What is the instantaneous speed ?Well, we don't know exactly, as the car may have been speeding up or slowing down during that time, but we can estimate: 20 m 1.6 s = 12.5 m/s = 45 km/h It is really still an average, but is close to an instantaneous speed. Constant SpeedWhen the speed does not change it is constant . For constant speed, the average and instantaneous speeds are the same. Because the direction is important velocity uses displacement instead of distance: Velocity = Displacement Time in a direction. Example: You walk from home to the shop in 100 seconds, what is your speed and what is your velocity?Speed = 220 m 100 s = 2.2 m/s Velocity = 130 m 100 s East = 1.3 m/s East You forgot your money so you turn around and go back home in 120 more seconds: what is your round-trip speed and velocity?The total time is 100 s + 120 s = 220 s: Speed = 440 m 220 s = 2.0 m/s Velocity = 0 m 220 s = 0 m/s Yes, the velocity is zero as you ended up where you started. Learn more at Vectors . Motion is relative. When we say something is "at rest" or "moving at 4 m/s" we forget to say "in relation to me" or "in relation to the ground", etc. Think about this: are you really standing still? You are on planet Earth which is spinning at 40,075 km per day (about 1675 km/h or 465 m/s), and moving around the Sun at about 100,000 km/h, which is itself moving through the Galaxy. Next time you are out walking, imagine you are still and it is the world that moves under your feet. Feels great. It is all relative!
 Problems on Calculating Speed | Speed Questions and AnswersSolve different types of problems on calculating speed and get acquainted with various models of questions asked in your exams. Be aware of the Formula to Calculate and Relationship between Speed Time and Distance. Practice Speed Problems on a regular basis so that you can be confident while attempting the exams. We even provided solutions for all the Questions provided and explained everything in detail for better understanding. Try to solve the Speed Questions on your own and then cross-check where you are lagging. We know the Speed of the Object is nothing but the distance traveled by the object in unit time. Formula to find out Speed is given by Speed = Distance/Time Word Problems on Calculating Speed1. A man walks 25 km in 6 hours. Find the speed of the man? Solution: Distance traveled = 25 km Time taken to travel = 6 hours Speed of Man = Distance traveled/Time taken = 25km/6hr = 4.16 km/hr Therefore, a man travels at a speed of 4.16 km/hr 2. A car covers a distance of 420 m in 1 minute whereas a train covers 70 km in 30 minutes. Find the ratio of their speeds? Solution: Speed of the Car = Distance Traveled/Time Taken = 420m/60 sec = 7 m/sec Speed of the Train = Distance Traveled/Time Taken = 70 km/1/2 hr = 140 km/hr To convert it into m/sec multiply with 5/18 = 140*5/18 = 38.8 m/sec = 39 m/sec (Approx) Ratio of Speeds = 7:39 3. A car moves from A to B at a speed of 70 km/hr and comes back from B to A at a speed of 40 km/hr. Find its average speed during the journey? Solution: Since the distance traveled is the same the Average Speed= (x+y)/2 where x, y are two different speeds Substitute the Speeds in the given formula Average Speed = (70+40)/2 = 110/2 = 55 km/hr The Average Speed of the Car is 55 km/hr 4. A bus covers a certain distance in 45 minutes if it runs at a speed of 50 km/hr. What must be the speed of the bus in order to reduce the time of journey by 20 minutes? Solution: Speed = Distance/Time 50 = x/3/4 50 = 4x/3 4x = 150 x = 150/4 = 37.5 km Now by applying the same formula we can find the speed Now, time = 40 mins or 0.66 hr since the journey is reduced by 20 mins S = Distance/Time = 37.5/0.66 = 56.81 km/hr 5. Ram traveled 200 km in 3 hours by train and then traveled 140 km in 3 hours by car and 5 km in 1/2 hour by cycle. What is the average speed during the whole journey? Solution: Distance traveled by Train is 200 km in 3 hours Distance Traveled by Car is 140 km in 3 hours Distance Traveled by Cycle is 5 km in 1/2 hour Average Speed = Total Distance/Total Time = (200+140+5)/(3+3+1/2) = 345/6 1/2 = 345/(13/2)” = 345*2/13 = 53.07 km/hr 6. A train covers 150 km in 3 hours. Find its speed? Solution: Speed = Distance/Time = 150 km/3 hr = 50 km/hr Therefore, Speed of the Train is 50 km/hr. Leave a Comment Cancel ReplyYou must be logged in to post a comment. Distance, Time and Speed Word Problems | GMAT GRE MathsBefore you get into distance, time and speed word problems, check out how you can add a little power to your resume by getting our mini-MBA certificate. Problems involving Time, Distance and Speed are solved based on one simple formula. Distance = Speed * Time Which implies → Speed = Distance / Time and Time = Distance / Speed Let us take a look at some simple examples of distance, time and speed problems. Example 1. A boy walks at a speed of 4 kmph. How much time does he take to walk a distance of 20 km? Time = Distance / speed = 20/4 = 5 hours. Example 2. A cyclist covers a distance of 15 miles in 2 hours. Calculate his speed. Speed = Distance/time = 15/2 = 7.5 miles per hour. Example 3. A car takes 4 hours to cover a distance, if it travels at a speed of 40 mph. What should be its speed to cover the same distance in 1.5 hours? Distance covered = 4*40 = 160 miles Speed required to cover the same distance in 1.5 hours = 160/1.5 = 106.66 mph Now, take a look at the following example: Example 4. If a person walks at 4 mph, he covers a certain distance. If he walks at 9 mph, he covers 7.5 miles more. How much distance did he actually cover? Now we can see that the direct application of our usual formula Distance = Speed * Time or its variations cannot be done in this case and we need to put in extra effort to calculate the given parameters. Let us see how this question can be solved. For these kinds of questions, a table like this might make it easier to solve.
Let the distance covered by that person be ‘d’. Walking at 4 mph and covering a distance ‘d’ is done in a time of ‘d/4’ IF he walks at 9 mph, he covers 7.5 miles more than the actual distance d, which is ‘d+7.5’. He does this in a time of (d+7.5)/9. Since the time is same in both the cases → d/4 = (d+7.5)/9 → 9d = 4(d+7.5) → 9d=4d+30 → d = 6. So, he covered a distance of 6 miles in 1.5 hours. Example 5. A train is going at 1/3 of its usual speed and it takes an extra 30 minutes to reach its destination. Find its usual time to cover the same distance. Here, we see that the distance is same. Let us assume that its usual speed is ‘s’ and time is ‘t’, then
s*t = (1/3)s*(t+30) → t = t/3 + 10 → t = 15. So the actual time taken to cover the distance is 15 minutes. Note: Note the time is expressed in terms of ‘minutes’. When we express distance in terms of miles or kilometers, time is expressed in terms of hours and has to be converted into appropriate units of measurement. Solved Questions on TrainsExample 1. X and Y are two stations which are 320 miles apart. A train starts at a certain time from X and travels towards Y at 70 mph. After 2 hours, another train starts from Y and travels towards X at 20 mph. At what time do they meet? Let the time after which they meet be ‘t’ hours. Then the time travelled by second train becomes ‘t-2’. Distance covered by first train+Distance covered by second train = 320 miles 70t+20(t-2) = 320 Solving this gives t = 4. So the two trains meet after 4 hours. Example 2. A train leaves from a station and moves at a certain speed. After 2 hours, another train leaves from the same station and moves in the same direction at a speed of 60 mph. If it catches up with the first train in 4 hours, what is the speed of the first train? Let the speed of the first train be ‘s’. Distance covered by the first train in (2+4) hours = Distance covered by second train in 4 hours Therefore, 6s = 60*4 Solving which gives s=40. So the slower train is moving at the rate of 40 mph. Questions on Boats/AirplanesFor problems with boats and streams, Speed of the boat upstream (against the current) = Speed of the boat in still water – speed of the stream [As the stream obstructs the speed of the boat in still water, its speed has to be subtracted from the usual speed of the boat] Speed of the boat downstream (along with the current) = Speed of the boat in still water + speed of the stream [As the stream pushes the boat and makes it easier for the boat to reach the destination faster, speed of the stream has to be added] Similarly, for airplanes travelling with/against the wind, Speed of the plane with the wind = speed of the plane + speed of the wind Speed of the plane against the wind = speed of the plane – speed of the wind Let us look at some examples. Example 1. A man travels at 3 mph in still water. If the current’s velocity is 1 mph, it takes 3 hours to row to a place and come back. How far is the place? Let the distance be ‘d’ miles. Time taken to cover the distance upstream + Time taken to cover the distance downstream = 3 Speed upstream = 3-1 = 2 mph Speed downstream = 3+1 = 4 mph So, our equation would be d/2 + d/4 = 3 → solving which, we get d = 4 miles. Example 2. With the wind, an airplane covers a distance of 2400 kms in 4 hours and against the wind in 6 hours. What is the speed of the plane and that of the wind? Let the speed of the plane be ‘a’ and that of the wind be ‘w’. Our table looks like this:
4(a+w) = 2400 and 6(a-w) = 2400 Expressing one unknown variable in terms of the other makes it easier to solve, which means a+w = 600 → w=600-a Substituting the value of w in the second equation, a-(600-a) = 400 → a = 500 The speed of the plane is 500 kmph and that of the wind is 100 kmph. More solved examples on Speed, Distance and TimeExample 1. A boy travelled by train which moved at the speed of 30 mph. He then boarded a bus which moved at the speed of 40 mph and reached his destination. The entire distance covered was 100 miles and the entire duration of the journey was 3 hours. Find the distance he travelled by bus.
Let the time taken by the train be ‘t’. Then that of bus is ‘3-t’. The entire distance covered was 100 miles So, 30t + 40(3-t) = 100 Solving which gives t=2. Substituting the value of t in 40(3-t), we get the distance travelled by bus is 40 miles. Alternatively, we can add the time and equate it to 3 hours, which directly gives the distance. d/30 + (100-d)/40 = 3 Solving which gives d = 60, which is the distance travelled by train. 100-60 = 40 miles is the distance travelled by bus. Example 2. A plane covered a distance of 630 miles in 6 hours. For the first part of the trip, the average speed was 100 mph and for the second part of the trip, the average speed was 110 mph. what is the time it flew at each speed? Our table looks like this.
Assuming the distance covered in the 1 st part of journey to be ‘d’, the distance covered in the second half becomes ‘630-d’. Assuming the time taken for the first part of the journey to be ‘t’, the time taken for the second half becomes ‘6-t’. From the first equation, d=100t The second equation is 630-d = 110(6-t). Substituting the value of d from the first equation, we get 630-100t = 110(6-t) Solving this gives t=3. So the plane flew the first part of the journey in 3 hours and the second part in 3 hours. Example 2. Two persons are walking towards each other on a walking path that is 20 miles long. One is walking at the rate of 3 mph and the other at 4 mph. After how much time will they meet each other?
Assuming the distance travelled by the first person to be ‘d’, the distance travelled by the second person is ’20-d’. The time is ‘t’ for both of them because when they meet, they would have walked for the same time. Since time is same, we can equate as d/3 = (20-d)/4 Solving this gives d=60/7 miles (8.5 miles approximately) Then t = 20/7 hours So the two persons meet after 2 6/7 hours. Practice Questions for you to solveProblem 1: Click here A boat covers a certain distance in 2 hours, while it comes back in 3 hours. If the speed of the stream is 4 kmph, what is the boat’s speed in still water? A) 30 kmph B) 20 kmph C) 15 kmph D) 40 kmph Answer 1: Click here Explanation Let the speed of the boat be ‘s’ kmph. Then, 2(s+4) = 3(s-4) → s = 20 Problem 2: Click here A cyclist travels for 3 hours, travelling for the first half of the journey at 12 mph and the second half at 15 mph. Find the total distance he covered. A) 30 miles B) 35 miles C) 40 miles D) 180 miles Answer 2: Click here Since it is mentioned, that the first ‘half’ of the journey is covered in 12 mph and the second in 15, the equation looks like (d/2)/12 + (d/2)/15 = 3 Solving this gives d = 40 miles Mini-MBA | Start here | Success stories | Reality check | Knowledgebase | Scholarships | Services Serious about higher ed? Follow us:  17 thoughts on “Distance, Time and Speed Word Problems | GMAT GRE Maths”Meera walked to school at a speed of 3 miles per hour. Once she reached the school, she realized that she forgot to bring her books, so rushed back home at a speed of 6 miles per hour. She then walked back to school at a speed of 4 miles per hour. All the times, she walked in the same route. please explain above problem When she walks faster the time she takes to reach her home and school is lower. There is nothing wrong with the statement. They never mentioned how long she took every time. a man covers a distance on a toy train.if the train moved 4km/hr faster,it would take 30 min. less. if it moved 2km/hr slower, it would have taken 20 min. more .find the distance. Let the speed be x. and time be y. A.T.Q, (x+4)(y-1/2)=d and (x-2)(y+1/3)=d. Equate these two and get the answer Could you explain how ? you have two equations and there are 3 variables. The 3rd equation is d=xy. Now, you have 3 equations with 3 unknowns. The variables x and y represent the usual speed and usual time to travel distance d. Speed comes out to be 20 km/hr and the time taken is 3 hrs. The distance traveled is 60 km. (s + 4) (t – 1/2)= st 1…new equotion = -1/2s + 4t = 2 (s – 2) (t + 1/3)= st 2…new equotion = 1/3s – 2t = 2/3 Multiply all by 6 1… -3s + 24t = 12 2… 2s – 12t = 4 Next, use elimination t= 3 Find s: -3s + 24t = 12 -3s + 24(3) = 12 -3s = -60 s= 20 st or distance = 3 x 20 = 60 km/h It’s probably the average speed that we are looking for here. Ave. Speed= total distance/ total time. Since it’s harder to look for one variable since both are absent, you can use, 3d/ d( V2V3 + V1V3 + V1V2/ V1V2V3) 2 girls meenu and priya start at the same time to ride from madurai to manamadurai, 60 km away.meenu travels 4kmph slower than priya. priya reaches manamadurai and at turns back meeting meenu 12km from manamaduai. find meenu’s speed? Hi, when the two girls meet, they have taken equal time to travel their respective distance. So, we just need to equate their time equations Distance travelled by Meenu = 60 -12 = 48 Distance travelled by Priya = 60 + 12 = 72 Let ‘s’ be the speed of Meenu Time taken by Meenu => t1 = 48/s Time taken by Priya => t2 = 72/(s+4) t1=t2 Thus, 48/s = 72/(s+4) => 24s = 192 => s = 8Km/hr A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 KMS away from A at the same time. On the way, however the train lost about 12.5 minutes while stopping at the stations. The speed of the car is: Let speed of the CAR BE x kmph. Then, speed of the train = 3/2(x) .’. 75/x – 75/(3/2)x= 125/(10*60) — subtracting the times travelled by two them hence trains wastage time therefore x= 120 kmph A cyclist completes a distance of 60 km at the same speed throughout. She travels 10 km in one hour. She stops every 20 km for one hour to have a break. What are the two variables involved in this situation? For the answer, not variables: 60km divided by 10km/h=6 hours 60 divided by 20= 3 hours 3 hours+6 hours= 9 hours Answer: 9 hours Let the length of the train to prod past a point be the intrinsic distance (D) of the train and its speed be S. Its speed, S in passing the electric pole of negligible length is = D/12. The length of the platform added to the intrinsic length of the train. So, the total distance = D + 200. The time = 20 secs. The Speed, S = (D + 200)/20 At constant speed, D/12 = (D + 200)/20 Cross-multiplying, 20D = 12D + 200*12 20D – 12D = 200*12; 8D = 200*12 D = 200*12/8 = 300m. 4th Aug, 2018 Can anyone solve this? Nathan and Philip agree to meet up at the park at 5:00 pm. Nathan lives 300 m due north of the park, and Philip lives 500 m due west of the park. Philip leaves his house at 4:54 pm and walks towards the park at a pace of 1.5 m/s, but Nathan loses track of time and doesn’t leave until 4:59 pm. Trying to avoid being too late, he jogs towards the park at 2.5 m/s. At what rate is the distance between the two friends changing 30 seconds after Nathan has departed? Leave a Comment Cancel replyJEE-IIT-NCERT Physics & MathWidget atas posting, average velocity and average speed problems and solutions. Problem #1
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All teams and organizations encounter challenges as they grow. There are problems that might occur for teams when it comes to miscommunication or resolving business-critical issues . You may face challenges around growth , design , user engagement, and even team culture and happiness. In short, problem-solving techniques should be part of every team’s skillset. Problem-solving methods are primarily designed to help a group or team through a process of first identifying problems and challenges , ideating possible solutions , and then evaluating the most suitable . Finding effective solutions to complex problems isn’t easy, but by using the right process and techniques, you can help your team be more efficient in the process. So how do you develop strategies that are engaging, and empower your team to solve problems effectively? In this blog post, we share a series of problem-solving tools you can use in your next workshop or team meeting. You’ll also find some tips for facilitating the process and how to enable others to solve complex problems. Let’s get started! How do you identify problems?How do you identify the right solution.
Complete problem-solving methods
Problem-solving warm-up activitiesClosing activities for a problem-solving process. Before you can move towards finding the right solution for a given problem, you first need to identify and define the problem you wish to solve. Here, you want to clearly articulate what the problem is and allow your group to do the same. Remember that everyone in a group is likely to have differing perspectives and alignment is necessary in order to help the group move forward. Identifying a problem accurately also requires that all members of a group are able to contribute their views in an open and safe manner. It can be scary for people to stand up and contribute, especially if the problems or challenges are emotive or personal in nature. Be sure to try and create a psychologically safe space for these kinds of discussions. Remember that problem analysis and further discussion are also important. Not taking the time to fully analyze and discuss a challenge can result in the development of solutions that are not fit for purpose or do not address the underlying issue. Successfully identifying and then analyzing a problem means facilitating a group through activities designed to help them clearly and honestly articulate their thoughts and produce usable insight. With this data, you might then produce a problem statement that clearly describes the problem you wish to be addressed and also state the goal of any process you undertake to tackle this issue. Finding solutions is the end goal of any process. Complex organizational challenges can only be solved with an appropriate solution but discovering them requires using the right problem-solving tool. After you’ve explored a problem and discussed ideas, you need to help a team discuss and choose the right solution. Consensus tools and methods such as those below help a group explore possible solutions before then voting for the best. They’re a great way to tap into the collective intelligence of the group for great results! Remember that the process is often iterative. Great problem solvers often roadtest a viable solution in a measured way to see what works too. While you might not get the right solution on your first try, the methods below help teams land on the most likely to succeed solution while also holding space for improvement. Every effective problem solving process begins with an agenda . A well-structured workshop is one of the best methods for successfully guiding a group from exploring a problem to implementing a solution. In SessionLab, it’s easy to go from an idea to a complete agenda . Start by dragging and dropping your core problem solving activities into place . Add timings, breaks and necessary materials before sharing your agenda with your colleagues. The resulting agenda will be your guide to an effective and productive problem solving session that will also help you stay organized on the day!  Tips for more effective problem solvingProblem-solving activities are only one part of the puzzle. While a great method can help unlock your team’s ability to solve problems, without a thoughtful approach and strong facilitation the solutions may not be fit for purpose. Let’s take a look at some problem-solving tips you can apply to any process to help it be a success! Clearly define the problemJumping straight to solutions can be tempting, though without first clearly articulating a problem, the solution might not be the right one. Many of the problem-solving activities below include sections where the problem is explored and clearly defined before moving on. This is a vital part of the problem-solving process and taking the time to fully define an issue can save time and effort later. A clear definition helps identify irrelevant information and it also ensures that your team sets off on the right track. Don’t jump to conclusionsIt’s easy for groups to exhibit cognitive bias or have preconceived ideas about both problems and potential solutions. Be sure to back up any problem statements or potential solutions with facts, research, and adequate forethought. The best techniques ask participants to be methodical and challenge preconceived notions. Make sure you give the group enough time and space to collect relevant information and consider the problem in a new way. By approaching the process with a clear, rational mindset, you’ll often find that better solutions are more forthcoming. Try different approachesProblems come in all shapes and sizes and so too should the methods you use to solve them. If you find that one approach isn’t yielding results and your team isn’t finding different solutions, try mixing it up. You’ll be surprised at how using a new creative activity can unblock your team and generate great solutions. Don’t take it personallyDepending on the nature of your team or organizational problems, it’s easy for conversations to get heated. While it’s good for participants to be engaged in the discussions, ensure that emotions don’t run too high and that blame isn’t thrown around while finding solutions. You’re all in it together, and even if your team or area is seeing problems, that isn’t necessarily a disparagement of you personally. Using facilitation skills to manage group dynamics is one effective method of helping conversations be more constructive. Get the right people in the roomYour problem-solving method is often only as effective as the group using it. Getting the right people on the job and managing the number of people present is important too! If the group is too small, you may not get enough different perspectives to effectively solve a problem. If the group is too large, you can go round and round during the ideation stages. Creating the right group makeup is also important in ensuring you have the necessary expertise and skillset to both identify and follow up on potential solutions. Carefully consider who to include at each stage to help ensure your problem-solving method is followed and positioned for success. Document everythingThe best solutions can take refinement, iteration, and reflection to come out. Get into a habit of documenting your process in order to keep all the learnings from the session and to allow ideas to mature and develop. Many of the methods below involve the creation of documents or shared resources. Be sure to keep and share these so everyone can benefit from the work done! Bring a facilitatorFacilitation is all about making group processes easier. With a subject as potentially emotive and important as problem-solving, having an impartial third party in the form of a facilitator can make all the difference in finding great solutions and keeping the process moving. Consider bringing a facilitator to your problem-solving session to get better results and generate meaningful solutions! Develop your problem-solving skillsIt takes time and practice to be an effective problem solver. While some roles or participants might more naturally gravitate towards problem-solving, it can take development and planning to help everyone create better solutions. You might develop a training program, run a problem-solving workshop or simply ask your team to practice using the techniques below. Check out our post on problem-solving skills to see how you and your group can develop the right mental process and be more resilient to issues too! Design a great agendaWorkshops are a great format for solving problems. With the right approach, you can focus a group and help them find the solutions to their own problems. But designing a process can be time-consuming and finding the right activities can be difficult. Check out our workshop planning guide to level-up your agenda design and start running more effective workshops. Need inspiration? Check out templates designed by expert facilitators to help you kickstart your process! In this section, we’ll look at in-depth problem-solving methods that provide a complete end-to-end process for developing effective solutions. These will help guide your team from the discovery and definition of a problem through to delivering the right solution. If you’re looking for an all-encompassing method or problem-solving model, these processes are a great place to start. They’ll ask your team to challenge preconceived ideas and adopt a mindset for solving problems more effectively.
Design Sprint 2.0
1. Six Thinking HatsIndividual approaches to solving a problem can be very different based on what team or role an individual holds. It can be easy for existing biases or perspectives to find their way into the mix, or for internal politics to direct a conversation. Six Thinking Hats is a classic method for identifying the problems that need to be solved and enables your team to consider them from different angles, whether that is by focusing on facts and data, creative solutions, or by considering why a particular solution might not work. Like all problem-solving frameworks, Six Thinking Hats is effective at helping teams remove roadblocks from a conversation or discussion and come to terms with all the aspects necessary to solve complex problems. 2. Lightning Decision JamFeatured courtesy of Jonathan Courtney of AJ&Smart Berlin, Lightning Decision Jam is one of those strategies that should be in every facilitation toolbox. Exploring problems and finding solutions is often creative in nature, though as with any creative process, there is the potential to lose focus and get lost. Unstructured discussions might get you there in the end, but it’s much more effective to use a method that creates a clear process and team focus. In Lightning Decision Jam, participants are invited to begin by writing challenges, concerns, or mistakes on post-its without discussing them before then being invited by the moderator to present them to the group. From there, the team vote on which problems to solve and are guided through steps that will allow them to reframe those problems, create solutions and then decide what to execute on. By deciding the problems that need to be solved as a team before moving on, this group process is great for ensuring the whole team is aligned and can take ownership over the next stages. Lightning Decision Jam (LDJ) #action #decision making #problem solving #issue analysis #innovation #design #remote-friendly The problem with anything that requires creative thinking is that it’s easy to get lost—lose focus and fall into the trap of having useless, open-ended, unstructured discussions. Here’s the most effective solution I’ve found: Replace all open, unstructured discussion with a clear process. What to use this exercise for: Anything which requires a group of people to make decisions, solve problems or discuss challenges. It’s always good to frame an LDJ session with a broad topic, here are some examples: The conversion flow of our checkout Our internal design process How we organise events Keeping up with our competition Improving sales flow 3. Problem Definition ProcessWhile problems can be complex, the problem-solving methods you use to identify and solve those problems can often be simple in design. By taking the time to truly identify and define a problem before asking the group to reframe the challenge as an opportunity, this method is a great way to enable change. Begin by identifying a focus question and exploring the ways in which it manifests before splitting into five teams who will each consider the problem using a different method: escape, reversal, exaggeration, distortion or wishful. Teams develop a problem objective and create ideas in line with their method before then feeding them back to the group. This method is great for enabling in-depth discussions while also creating space for finding creative solutions too! Problem Definition #problem solving #idea generation #creativity #online #remote-friendly A problem solving technique to define a problem, challenge or opportunity and to generate ideas. 4. The 5 WhysSometimes, a group needs to go further with their strategies and analyze the root cause at the heart of organizational issues. An RCA or root cause analysis is the process of identifying what is at the heart of business problems or recurring challenges. The 5 Whys is a simple and effective method of helping a group go find the root cause of any problem or challenge and conduct analysis that will deliver results. By beginning with the creation of a problem statement and going through five stages to refine it, The 5 Whys provides everything you need to truly discover the cause of an issue. The 5 Whys #hyperisland #innovation This simple and powerful method is useful for getting to the core of a problem or challenge. As the title suggests, the group defines a problems, then asks the question “why” five times, often using the resulting explanation as a starting point for creative problem solving. 5. World CafeWorld Cafe is a simple but powerful facilitation technique to help bigger groups to focus their energy and attention on solving complex problems. World Cafe enables this approach by creating a relaxed atmosphere where participants are able to self-organize and explore topics relevant and important to them which are themed around a central problem-solving purpose. Create the right atmosphere by modeling your space after a cafe and after guiding the group through the method, let them take the lead! Making problem-solving a part of your organization’s culture in the long term can be a difficult undertaking. More approachable formats like World Cafe can be especially effective in bringing people unfamiliar with workshops into the fold. World Cafe #hyperisland #innovation #issue analysis World Café is a simple yet powerful method, originated by Juanita Brown, for enabling meaningful conversations driven completely by participants and the topics that are relevant and important to them. Facilitators create a cafe-style space and provide simple guidelines. Participants then self-organize and explore a set of relevant topics or questions for conversation. 6. Discovery & Action Dialogue (DAD)One of the best approaches is to create a safe space for a group to share and discover practices and behaviors that can help them find their own solutions. With DAD, you can help a group choose which problems they wish to solve and which approaches they will take to do so. It’s great at helping remove resistance to change and can help get buy-in at every level too! This process of enabling frontline ownership is great in ensuring follow-through and is one of the methods you will want in your toolbox as a facilitator. Discovery & Action Dialogue (DAD) #idea generation #liberating structures #action #issue analysis #remote-friendly DADs make it easy for a group or community to discover practices and behaviors that enable some individuals (without access to special resources and facing the same constraints) to find better solutions than their peers to common problems. These are called positive deviant (PD) behaviors and practices. DADs make it possible for people in the group, unit, or community to discover by themselves these PD practices. DADs also create favorable conditions for stimulating participants’ creativity in spaces where they can feel safe to invent new and more effective practices. Resistance to change evaporates as participants are unleashed to choose freely which practices they will adopt or try and which problems they will tackle. DADs make it possible to achieve frontline ownership of solutions. 7. Design Sprint 2.0Want to see how a team can solve big problems and move forward with prototyping and testing solutions in a few days? The Design Sprint 2.0 template from Jake Knapp, author of Sprint, is a complete agenda for a with proven results. Developing the right agenda can involve difficult but necessary planning. Ensuring all the correct steps are followed can also be stressful or time-consuming depending on your level of experience. Use this complete 4-day workshop template if you are finding there is no obvious solution to your challenge and want to focus your team around a specific problem that might require a shortcut to launching a minimum viable product or waiting for the organization-wide implementation of a solution. 8. Open space technologyOpen space technology- developed by Harrison Owen – creates a space where large groups are invited to take ownership of their problem solving and lead individual sessions. Open space technology is a great format when you have a great deal of expertise and insight in the room and want to allow for different takes and approaches on a particular theme or problem you need to be solved. Start by bringing your participants together to align around a central theme and focus their efforts. Explain the ground rules to help guide the problem-solving process and then invite members to identify any issue connecting to the central theme that they are interested in and are prepared to take responsibility for. Once participants have decided on their approach to the core theme, they write their issue on a piece of paper, announce it to the group, pick a session time and place, and post the paper on the wall. As the wall fills up with sessions, the group is then invited to join the sessions that interest them the most and which they can contribute to, then you’re ready to begin! Everyone joins the problem-solving group they’ve signed up to, record the discussion and if appropriate, findings can then be shared with the rest of the group afterward. Open Space Technology #action plan #idea generation #problem solving #issue analysis #large group #online #remote-friendly Open Space is a methodology for large groups to create their agenda discerning important topics for discussion, suitable for conferences, community gatherings and whole system facilitation Techniques to identify and analyze problemsUsing a problem-solving method to help a team identify and analyze a problem can be a quick and effective addition to any workshop or meeting. While further actions are always necessary, you can generate momentum and alignment easily, and these activities are a great place to get started. We’ve put together this list of techniques to help you and your team with problem identification, analysis, and discussion that sets the foundation for developing effective solutions. Let’s take a look!
Individual and group perspectives are incredibly important, but what happens if people are set in their minds and need a change of perspective in order to approach a problem more effectively? Flip It is a method we love because it is both simple to understand and run, and allows groups to understand how their perspectives and biases are formed. Participants in Flip It are first invited to consider concerns, issues, or problems from a perspective of fear and write them on a flip chart. Then, the group is asked to consider those same issues from a perspective of hope and flip their understanding. No problem and solution is free from existing bias and by changing perspectives with Flip It, you can then develop a problem solving model quickly and effectively. Flip It! #gamestorming #problem solving #action Often, a change in a problem or situation comes simply from a change in our perspectives. Flip It! is a quick game designed to show players that perspectives are made, not born. 10. The Creativity DiceOne of the most useful problem solving skills you can teach your team is of approaching challenges with creativity, flexibility, and openness. Games like The Creativity Dice allow teams to overcome the potential hurdle of too much linear thinking and approach the process with a sense of fun and speed. In The Creativity Dice, participants are organized around a topic and roll a dice to determine what they will work on for a period of 3 minutes at a time. They might roll a 3 and work on investigating factual information on the chosen topic. They might roll a 1 and work on identifying the specific goals, standards, or criteria for the session. Encouraging rapid work and iteration while asking participants to be flexible are great skills to cultivate. Having a stage for idea incubation in this game is also important. Moments of pause can help ensure the ideas that are put forward are the most suitable. The Creativity Dice #creativity #problem solving #thiagi #issue analysis Too much linear thinking is hazardous to creative problem solving. To be creative, you should approach the problem (or the opportunity) from different points of view. You should leave a thought hanging in mid-air and move to another. This skipping around prevents premature closure and lets your brain incubate one line of thought while you consciously pursue another. 11. Fishbone AnalysisOrganizational or team challenges are rarely simple, and it’s important to remember that one problem can be an indication of something that goes deeper and may require further consideration to be solved. Fishbone Analysis helps groups to dig deeper and understand the origins of a problem. It’s a great example of a root cause analysis method that is simple for everyone on a team to get their head around. Participants in this activity are asked to annotate a diagram of a fish, first adding the problem or issue to be worked on at the head of a fish before then brainstorming the root causes of the problem and adding them as bones on the fish. Using abstractions such as a diagram of a fish can really help a team break out of their regular thinking and develop a creative approach. Fishbone Analysis #problem solving ##root cause analysis #decision making #online facilitation A process to help identify and understand the origins of problems, issues or observations. 12. Problem TreeEncouraging visual thinking can be an essential part of many strategies. By simply reframing and clarifying problems, a group can move towards developing a problem solving model that works for them. In Problem Tree, groups are asked to first brainstorm a list of problems – these can be design problems, team problems or larger business problems – and then organize them into a hierarchy. The hierarchy could be from most important to least important or abstract to practical, though the key thing with problem solving games that involve this aspect is that your group has some way of managing and sorting all the issues that are raised. Once you have a list of problems that need to be solved and have organized them accordingly, you’re then well-positioned for the next problem solving steps. Problem tree #define intentions #create #design #issue analysis A problem tree is a tool to clarify the hierarchy of problems addressed by the team within a design project; it represents high level problems or related sublevel problems. 13. SWOT AnalysisChances are you’ve heard of the SWOT Analysis before. This problem-solving method focuses on identifying strengths, weaknesses, opportunities, and threats is a tried and tested method for both individuals and teams. Start by creating a desired end state or outcome and bare this in mind – any process solving model is made more effective by knowing what you are moving towards. Create a quadrant made up of the four categories of a SWOT analysis and ask participants to generate ideas based on each of those quadrants. Once you have those ideas assembled in their quadrants, cluster them together based on their affinity with other ideas. These clusters are then used to facilitate group conversations and move things forward. SWOT analysis #gamestorming #problem solving #action #meeting facilitation The SWOT Analysis is a long-standing technique of looking at what we have, with respect to the desired end state, as well as what we could improve on. It gives us an opportunity to gauge approaching opportunities and dangers, and assess the seriousness of the conditions that affect our future. When we understand those conditions, we can influence what comes next. 14. Agreement-Certainty MatrixNot every problem-solving approach is right for every challenge, and deciding on the right method for the challenge at hand is a key part of being an effective team. The Agreement Certainty matrix helps teams align on the nature of the challenges facing them. By sorting problems from simple to chaotic, your team can understand what methods are suitable for each problem and what they can do to ensure effective results. If you are already using Liberating Structures techniques as part of your problem-solving strategy, the Agreement-Certainty Matrix can be an invaluable addition to your process. We’ve found it particularly if you are having issues with recurring problems in your organization and want to go deeper in understanding the root cause. Agreement-Certainty Matrix #issue analysis #liberating structures #problem solving You can help individuals or groups avoid the frequent mistake of trying to solve a problem with methods that are not adapted to the nature of their challenge. The combination of two questions makes it possible to easily sort challenges into four categories: simple, complicated, complex , and chaotic . A problem is simple when it can be solved reliably with practices that are easy to duplicate. It is complicated when experts are required to devise a sophisticated solution that will yield the desired results predictably. A problem is complex when there are several valid ways to proceed but outcomes are not predictable in detail. Chaotic is when the context is too turbulent to identify a path forward. A loose analogy may be used to describe these differences: simple is like following a recipe, complicated like sending a rocket to the moon, complex like raising a child, and chaotic is like the game “Pin the Tail on the Donkey.” The Liberating Structures Matching Matrix in Chapter 5 can be used as the first step to clarify the nature of a challenge and avoid the mismatches between problems and solutions that are frequently at the root of chronic, recurring problems. Organizing and charting a team’s progress can be important in ensuring its success. SQUID (Sequential Question and Insight Diagram) is a great model that allows a team to effectively switch between giving questions and answers and develop the skills they need to stay on track throughout the process. Begin with two different colored sticky notes – one for questions and one for answers – and with your central topic (the head of the squid) on the board. Ask the group to first come up with a series of questions connected to their best guess of how to approach the topic. Ask the group to come up with answers to those questions, fix them to the board and connect them with a line. After some discussion, go back to question mode by responding to the generated answers or other points on the board. It’s rewarding to see a diagram grow throughout the exercise, and a completed SQUID can provide a visual resource for future effort and as an example for other teams. SQUID #gamestorming #project planning #issue analysis #problem solving When exploring an information space, it’s important for a group to know where they are at any given time. By using SQUID, a group charts out the territory as they go and can navigate accordingly. SQUID stands for Sequential Question and Insight Diagram. 16. Speed BoatTo continue with our nautical theme, Speed Boat is a short and sweet activity that can help a team quickly identify what employees, clients or service users might have a problem with and analyze what might be standing in the way of achieving a solution. Methods that allow for a group to make observations, have insights and obtain those eureka moments quickly are invaluable when trying to solve complex problems. In Speed Boat, the approach is to first consider what anchors and challenges might be holding an organization (or boat) back. Bonus points if you are able to identify any sharks in the water and develop ideas that can also deal with competitors! Speed Boat #gamestorming #problem solving #action Speedboat is a short and sweet way to identify what your employees or clients don’t like about your product/service or what’s standing in the way of a desired goal. 17. The Journalistic SixSome of the most effective ways of solving problems is by encouraging teams to be more inclusive and diverse in their thinking. Based on the six key questions journalism students are taught to answer in articles and news stories, The Journalistic Six helps create teams to see the whole picture. By using who, what, when, where, why, and how to facilitate the conversation and encourage creative thinking, your team can make sure that the problem identification and problem analysis stages of the are covered exhaustively and thoughtfully. Reporter’s notebook and dictaphone optional. The Journalistic Six – Who What When Where Why How #idea generation #issue analysis #problem solving #online #creative thinking #remote-friendly A questioning method for generating, explaining, investigating ideas. 18. LEGO ChallengeNow for an activity that is a little out of the (toy) box. LEGO Serious Play is a facilitation methodology that can be used to improve creative thinking and problem-solving skills. The LEGO Challenge includes giving each member of the team an assignment that is hidden from the rest of the group while they create a structure without speaking. What the LEGO challenge brings to the table is a fun working example of working with stakeholders who might not be on the same page to solve problems. Also, it’s LEGO! Who doesn’t love LEGO! LEGO Challenge #hyperisland #team A team-building activity in which groups must work together to build a structure out of LEGO, but each individual has a secret “assignment” which makes the collaborative process more challenging. It emphasizes group communication, leadership dynamics, conflict, cooperation, patience and problem solving strategy. 19. What, So What, Now What?If not carefully managed, the problem identification and problem analysis stages of the problem-solving process can actually create more problems and misunderstandings. The What, So What, Now What? problem-solving activity is designed to help collect insights and move forward while also eliminating the possibility of disagreement when it comes to identifying, clarifying, and analyzing organizational or work problems. Facilitation is all about bringing groups together so that might work on a shared goal and the best problem-solving strategies ensure that teams are aligned in purpose, if not initially in opinion or insight. Throughout the three steps of this game, you give everyone on a team to reflect on a problem by asking what happened, why it is important, and what actions should then be taken. This can be a great activity for bringing our individual perceptions about a problem or challenge and contextualizing it in a larger group setting. This is one of the most important problem-solving skills you can bring to your organization. W³ – What, So What, Now What? #issue analysis #innovation #liberating structures You can help groups reflect on a shared experience in a way that builds understanding and spurs coordinated action while avoiding unproductive conflict. It is possible for every voice to be heard while simultaneously sifting for insights and shaping new direction. Progressing in stages makes this practical—from collecting facts about What Happened to making sense of these facts with So What and finally to what actions logically follow with Now What . The shared progression eliminates most of the misunderstandings that otherwise fuel disagreements about what to do. Voila! 20. JournalistsProblem analysis can be one of the most important and decisive stages of all problem-solving tools. Sometimes, a team can become bogged down in the details and are unable to move forward. Journalists is an activity that can avoid a group from getting stuck in the problem identification or problem analysis stages of the process. In Journalists, the group is invited to draft the front page of a fictional newspaper and figure out what stories deserve to be on the cover and what headlines those stories will have. By reframing how your problems and challenges are approached, you can help a team move productively through the process and be better prepared for the steps to follow. Journalists #vision #big picture #issue analysis #remote-friendly This is an exercise to use when the group gets stuck in details and struggles to see the big picture. Also good for defining a vision. Problem-solving techniques for developing solutionsThe success of any problem-solving process can be measured by the solutions it produces. After you’ve defined the issue, explored existing ideas, and ideated, it’s time to narrow down to the correct solution. Use these problem-solving techniques when you want to help your team find consensus, compare possible solutions, and move towards taking action on a particular problem.
21. MindspinBrainstorming is part of the bread and butter of the problem-solving process and all problem-solving strategies benefit from getting ideas out and challenging a team to generate solutions quickly. With Mindspin, participants are encouraged not only to generate ideas but to do so under time constraints and by slamming down cards and passing them on. By doing multiple rounds, your team can begin with a free generation of possible solutions before moving on to developing those solutions and encouraging further ideation. This is one of our favorite problem-solving activities and can be great for keeping the energy up throughout the workshop. Remember the importance of helping people become engaged in the process – energizing problem-solving techniques like Mindspin can help ensure your team stays engaged and happy, even when the problems they’re coming together to solve are complex. MindSpin #teampedia #idea generation #problem solving #action A fast and loud method to enhance brainstorming within a team. Since this activity has more than round ideas that are repetitive can be ruled out leaving more creative and innovative answers to the challenge. 22. Improved SolutionsAfter a team has successfully identified a problem and come up with a few solutions, it can be tempting to call the work of the problem-solving process complete. That said, the first solution is not necessarily the best, and by including a further review and reflection activity into your problem-solving model, you can ensure your group reaches the best possible result. One of a number of problem-solving games from Thiagi Group, Improved Solutions helps you go the extra mile and develop suggested solutions with close consideration and peer review. By supporting the discussion of several problems at once and by shifting team roles throughout, this problem-solving technique is a dynamic way of finding the best solution. Improved Solutions #creativity #thiagi #problem solving #action #team You can improve any solution by objectively reviewing its strengths and weaknesses and making suitable adjustments. In this creativity framegame, you improve the solutions to several problems. To maintain objective detachment, you deal with a different problem during each of six rounds and assume different roles (problem owner, consultant, basher, booster, enhancer, and evaluator) during each round. At the conclusion of the activity, each player ends up with two solutions to her problem. 23. Four Step SketchCreative thinking and visual ideation does not need to be confined to the opening stages of your problem-solving strategies. Exercises that include sketching and prototyping on paper can be effective at the solution finding and development stage of the process, and can be great for keeping a team engaged. By going from simple notes to a crazy 8s round that involves rapidly sketching 8 variations on their ideas before then producing a final solution sketch, the group is able to iterate quickly and visually. Problem-solving techniques like Four-Step Sketch are great if you have a group of different thinkers and want to change things up from a more textual or discussion-based approach. Four-Step Sketch #design sprint #innovation #idea generation #remote-friendly The four-step sketch is an exercise that helps people to create well-formed concepts through a structured process that includes: Review key information Start design work on paper, Consider multiple variations , Create a detailed solution . This exercise is preceded by a set of other activities allowing the group to clarify the challenge they want to solve. See how the Four Step Sketch exercise fits into a Design Sprint 24. 15% SolutionsSome problems are simpler than others and with the right problem-solving activities, you can empower people to take immediate actions that can help create organizational change. Part of the liberating structures toolkit, 15% solutions is a problem-solving technique that focuses on finding and implementing solutions quickly. A process of iterating and making small changes quickly can help generate momentum and an appetite for solving complex problems. Problem-solving strategies can live and die on whether people are onboard. Getting some quick wins is a great way of getting people behind the process. It can be extremely empowering for a team to realize that problem-solving techniques can be deployed quickly and easily and delineate between things they can positively impact and those things they cannot change. 15% Solutions #action #liberating structures #remote-friendly You can reveal the actions, however small, that everyone can do immediately. At a minimum, these will create momentum, and that may make a BIG difference. 15% Solutions show that there is no reason to wait around, feel powerless, or fearful. They help people pick it up a level. They get individuals and the group to focus on what is within their discretion instead of what they cannot change. With a very simple question, you can flip the conversation to what can be done and find solutions to big problems that are often distributed widely in places not known in advance. Shifting a few grains of sand may trigger a landslide and change the whole landscape. 25. How-Now-Wow MatrixThe problem-solving process is often creative, as complex problems usually require a change of thinking and creative response in order to find the best solutions. While it’s common for the first stages to encourage creative thinking, groups can often gravitate to familiar solutions when it comes to the end of the process. When selecting solutions, you don’t want to lose your creative energy! The How-Now-Wow Matrix from Gamestorming is a great problem-solving activity that enables a group to stay creative and think out of the box when it comes to selecting the right solution for a given problem. Problem-solving techniques that encourage creative thinking and the ideation and selection of new solutions can be the most effective in organisational change. Give the How-Now-Wow Matrix a go, and not just for how pleasant it is to say out loud. How-Now-Wow Matrix #gamestorming #idea generation #remote-friendly When people want to develop new ideas, they most often think out of the box in the brainstorming or divergent phase. However, when it comes to convergence, people often end up picking ideas that are most familiar to them. This is called a ‘creative paradox’ or a ‘creadox’. The How-Now-Wow matrix is an idea selection tool that breaks the creadox by forcing people to weigh each idea on 2 parameters. 26. Impact and Effort MatrixAll problem-solving techniques hope to not only find solutions to a given problem or challenge but to find the best solution. When it comes to finding a solution, groups are invited to put on their decision-making hats and really think about how a proposed idea would work in practice. The Impact and Effort Matrix is one of the problem-solving techniques that fall into this camp, empowering participants to first generate ideas and then categorize them into a 2×2 matrix based on impact and effort. Activities that invite critical thinking while remaining simple are invaluable. Use the Impact and Effort Matrix to move from ideation and towards evaluating potential solutions before then committing to them. Impact and Effort Matrix #gamestorming #decision making #action #remote-friendly In this decision-making exercise, possible actions are mapped based on two factors: effort required to implement and potential impact. Categorizing ideas along these lines is a useful technique in decision making, as it obliges contributors to balance and evaluate suggested actions before committing to them. 27. DotmocracyIf you’ve followed each of the problem-solving steps with your group successfully, you should move towards the end of your process with heaps of possible solutions developed with a specific problem in mind. But how do you help a group go from ideation to putting a solution into action? Dotmocracy – or Dot Voting -is a tried and tested method of helping a team in the problem-solving process make decisions and put actions in place with a degree of oversight and consensus. One of the problem-solving techniques that should be in every facilitator’s toolbox, Dot Voting is fast and effective and can help identify the most popular and best solutions and help bring a group to a decision effectively. Dotmocracy #action #decision making #group prioritization #hyperisland #remote-friendly Dotmocracy is a simple method for group prioritization or decision-making. It is not an activity on its own, but a method to use in processes where prioritization or decision-making is the aim. The method supports a group to quickly see which options are most popular or relevant. The options or ideas are written on post-its and stuck up on a wall for the whole group to see. Each person votes for the options they think are the strongest, and that information is used to inform a decision. All facilitators know that warm-ups and icebreakers are useful for any workshop or group process. Problem-solving workshops are no different. Use these problem-solving techniques to warm up a group and prepare them for the rest of the process. Activating your group by tapping into some of the top problem-solving skills can be one of the best ways to see great outcomes from your session.
28. Check-in / Check-outSolid processes are planned from beginning to end, and the best facilitators know that setting the tone and establishing a safe, open environment can be integral to a successful problem-solving process. Check-in / Check-out is a great way to begin and/or bookend a problem-solving workshop. Checking in to a session emphasizes that everyone will be seen, heard, and expected to contribute. If you are running a series of meetings, setting a consistent pattern of checking in and checking out can really help your team get into a groove. We recommend this opening-closing activity for small to medium-sized groups though it can work with large groups if they’re disciplined! Check-in / Check-out #team #opening #closing #hyperisland #remote-friendly Either checking-in or checking-out is a simple way for a team to open or close a process, symbolically and in a collaborative way. Checking-in/out invites each member in a group to be present, seen and heard, and to express a reflection or a feeling. Checking-in emphasizes presence, focus and group commitment; checking-out emphasizes reflection and symbolic closure. 29. Doodling TogetherThinking creatively and not being afraid to make suggestions are important problem-solving skills for any group or team, and warming up by encouraging these behaviors is a great way to start. Doodling Together is one of our favorite creative ice breaker games – it’s quick, effective, and fun and can make all following problem-solving steps easier by encouraging a group to collaborate visually. By passing cards and adding additional items as they go, the workshop group gets into a groove of co-creation and idea development that is crucial to finding solutions to problems. Doodling Together #collaboration #creativity #teamwork #fun #team #visual methods #energiser #icebreaker #remote-friendly Create wild, weird and often funny postcards together & establish a group’s creative confidence. 30. Show and TellYou might remember some version of Show and Tell from being a kid in school and it’s a great problem-solving activity to kick off a session. Asking participants to prepare a little something before a workshop by bringing an object for show and tell can help them warm up before the session has even begun! Games that include a physical object can also help encourage early engagement before moving onto more big-picture thinking. By asking your participants to tell stories about why they chose to bring a particular item to the group, you can help teams see things from new perspectives and see both differences and similarities in the way they approach a topic. Great groundwork for approaching a problem-solving process as a team! Show and Tell #gamestorming #action #opening #meeting facilitation Show and Tell taps into the power of metaphors to reveal players’ underlying assumptions and associations around a topic The aim of the game is to get a deeper understanding of stakeholders’ perspectives on anything—a new project, an organizational restructuring, a shift in the company’s vision or team dynamic. 31. ConstellationsWho doesn’t love stars? Constellations is a great warm-up activity for any workshop as it gets people up off their feet, energized, and ready to engage in new ways with established topics. It’s also great for showing existing beliefs, biases, and patterns that can come into play as part of your session. Using warm-up games that help build trust and connection while also allowing for non-verbal responses can be great for easing people into the problem-solving process and encouraging engagement from everyone in the group. Constellations is great in large spaces that allow for movement and is definitely a practical exercise to allow the group to see patterns that are otherwise invisible. Constellations #trust #connection #opening #coaching #patterns #system Individuals express their response to a statement or idea by standing closer or further from a central object. Used with teams to reveal system, hidden patterns, perspectives. 32. Draw a TreeProblem-solving games that help raise group awareness through a central, unifying metaphor can be effective ways to warm-up a group in any problem-solving model. Draw a Tree is a simple warm-up activity you can use in any group and which can provide a quick jolt of energy. Start by asking your participants to draw a tree in just 45 seconds – they can choose whether it will be abstract or realistic. Once the timer is up, ask the group how many people included the roots of the tree and use this as a means to discuss how we can ignore important parts of any system simply because they are not visible. All problem-solving strategies are made more effective by thinking of problems critically and by exposing things that may not normally come to light. Warm-up games like Draw a Tree are great in that they quickly demonstrate some key problem-solving skills in an accessible and effective way. Draw a Tree #thiagi #opening #perspectives #remote-friendly With this game you can raise awarness about being more mindful, and aware of the environment we live in. Each step of the problem-solving workshop benefits from an intelligent deployment of activities, games, and techniques. Bringing your session to an effective close helps ensure that solutions are followed through on and that you also celebrate what has been achieved. Here are some problem-solving activities you can use to effectively close a workshop or meeting and ensure the great work you’ve done can continue afterward.
How do I conclude a problem-solving process?All good things must come to an end. With the bulk of the work done, it can be tempting to conclude your workshop swiftly and without a moment to debrief and align. This can be problematic in that it doesn’t allow your team to fully process the results or reflect on the process. At the end of an effective session, your team will have gone through a process that, while productive, can be exhausting. It’s important to give your group a moment to take a breath, ensure that they are clear on future actions, and provide short feedback before leaving the space. The primary purpose of any problem-solving method is to generate solutions and then implement them. Be sure to take the opportunity to ensure everyone is aligned and ready to effectively implement the solutions you produced in the workshop. Remember that every process can be improved and by giving a short moment to collect feedback in the session, you can further refine your problem-solving methods and see further success in the future too. 33. One Breath FeedbackMaintaining attention and focus during the closing stages of a problem-solving workshop can be tricky and so being concise when giving feedback can be important. It’s easy to incur “death by feedback” should some team members go on for too long sharing their perspectives in a quick feedback round. One Breath Feedback is a great closing activity for workshops. You give everyone an opportunity to provide feedback on what they’ve done but only in the space of a single breath. This keeps feedback short and to the point and means that everyone is encouraged to provide the most important piece of feedback to them. One breath feedback #closing #feedback #action This is a feedback round in just one breath that excels in maintaining attention: each participants is able to speak during just one breath … for most people that’s around 20 to 25 seconds … unless of course you’ve been a deep sea diver in which case you’ll be able to do it for longer. 34. Who What When MatrixMatrices feature as part of many effective problem-solving strategies and with good reason. They are easily recognizable, simple to use, and generate results. The Who What When Matrix is a great tool to use when closing your problem-solving session by attributing a who, what and when to the actions and solutions you have decided upon. The resulting matrix is a simple, easy-to-follow way of ensuring your team can move forward. Great solutions can’t be enacted without action and ownership. Your problem-solving process should include a stage for allocating tasks to individuals or teams and creating a realistic timeframe for those solutions to be implemented or checked out. Use this method to keep the solution implementation process clear and simple for all involved. Who/What/When Matrix #gamestorming #action #project planning With Who/What/When matrix, you can connect people with clear actions they have defined and have committed to. 35. Response cardsGroup discussion can comprise the bulk of most problem-solving activities and by the end of the process, you might find that your team is talked out! Providing a means for your team to give feedback with short written notes can ensure everyone is head and can contribute without the need to stand up and talk. Depending on the needs of the group, giving an alternative can help ensure everyone can contribute to your problem-solving model in the way that makes the most sense for them. Response Cards is a great way to close a workshop if you are looking for a gentle warm-down and want to get some swift discussion around some of the feedback that is raised. Response Cards #debriefing #closing #structured sharing #questions and answers #thiagi #action It can be hard to involve everyone during a closing of a session. Some might stay in the background or get unheard because of louder participants. However, with the use of Response Cards, everyone will be involved in providing feedback or clarify questions at the end of a session. Save time and effort discovering the right solutionsA structured problem solving process is a surefire way of solving tough problems, discovering creative solutions and driving organizational change. But how can you design for successful outcomes? With SessionLab, it’s easy to design engaging workshops that deliver results. Drag, drop and reorder blocks to build your agenda. When you make changes or update your agenda, your session timing adjusts automatically , saving you time on manual adjustments. Collaborating with stakeholders or clients? Share your agenda with a single click and collaborate in real-time. No more sending documents back and forth over email. Explore how to use SessionLab to design effective problem solving workshops or watch this five minute video to see the planner in action!  Over to youThe problem-solving process can often be as complicated and multifaceted as the problems they are set-up to solve. With the right problem-solving techniques and a mix of creative exercises designed to guide discussion and generate purposeful ideas, we hope we’ve given you the tools to find the best solutions as simply and easily as possible. Is there a problem-solving technique that you are missing here? Do you have a favorite activity or method you use when facilitating? Let us know in the comments below, we’d love to hear from you!  thank you very much for these excellent techniques  Certainly wonderful article, very detailed. Shared!  Your list of techniques for problem solving can be helpfully extended by adding TRIZ to the list of techniques. TRIZ has 40 problem solving techniques derived from methods inventros and patent holders used to get new patents. About 10-12 are general approaches. many organization sponsor classes in TRIZ that are used to solve business problems or general organiztational problems. You can take a look at TRIZ and dwonload a free internet booklet to see if you feel it shound be included per your selection process. Leave a Comment Cancel replyYour email address will not be published. Required fields are marked *  Going from a mere idea to a workshop that delivers results for your clients can feel like a daunting task. In this piece, we will shine a light on all the work behind the scenes and help you learn how to plan a workshop from start to finish. On a good day, facilitation can feel like effortless magic, but that is mostly the result of backstage work, foresight, and a lot of careful planning. Read on to learn a step-by-step approach to breaking the process of planning a workshop into small, manageable chunks. The flow starts with the first meeting with a client to define the purposes of a workshop.…  How does learning work? A clever 9-year-old once told me: “I know I am learning something new when I am surprised.” The science of adult learning tells us that, in order to learn new skills (which, unsurprisingly, is harder for adults to do than kids) grown-ups need to first get into a specific headspace. In a business, this approach is often employed in a training session where employees learn new skills or work on professional development. But how do you ensure your training is effective? In this guide, we'll explore how to create an effective training session plan and run engaging training sessions. As team leader, project manager, or consultant,…  Facilitation is more and more recognized as a key component of work, as employers and society are faced with bigger and more complex problems and ideas. From facilitating meetings to big, multi-stakeholder strategy development workshops, the facilitator's skillset is more and more in demand. In this article, we will go through a list of the best online facilitation resources, including newsletters, podcasts, communities, and 10 free toolkits you can bookmark and read to upskill and improve your facilitation practice. When designing activities and workshops, you'll probably start by using templates and methods you are familiar with. Soon enough, you'll need to expand your range and look for facilitation methods and… Design your next workshop with SessionLabJoin the 150,000 facilitators using SessionLab Sign up for free
8 Reasons Why Your Internet is Slow (and How to Fix It)Expert tips to banish slow internet speeds  Tired of endless buffering circles, slow downloads, and laggy browsing? Slow internet today means slow everything, but who has an extra afternoon to sacrifice to the tech troubleshooting gods? Fortunately, it’s very possible there’s a quick and easy fix for your sluggish home network. Your slow internet speeds are probably caused by one of these eight very common network issues. You can fix most of these issues yourself; some only take a few minutes—we’ll start with those. It is possible that you have a more complicated issue on your hands; we’ll go over these instances, too, and provide you with some additional in-depth troubleshooting resources. Fed up with slow internet? Check out your other options. Enter your zip code below to see if a faster plan is available in your area. Jump to: Why is your internet so slow? | How to fix your slow internet connection | Other reasons your internet is slow | More ways to speed up slow internet | FAQ Why is your internet so slow?We provide more detail on each of these potential internet slowdown causes further down the page. Click on an issue to auto-scroll to the solution. Here are the most common reasons for a slow internet connection: 1. You need to restart your modem and router Equipment restarts are hands down the most effective internet troubleshooting solution. This should always be your first step. 2. Your home network is congested Congestion happens when you overload your internet connection with more traffic than it can handle. To fix it, you can either lower your internet usage or upgrade to a faster plan. 3. You need a stronger Wi-Fi signal You experience a weak Wi-Fi signal when you’re too far from your router, when the signal is forced to pass through obstructive materials, or when other Wi-Fi networks and electronic devices introduce interference. You can fix it by extending your Wi-Fi range, choosing a better spot for your router, or adjusting your router’s settings. 4. Your network cables are damaged or loose Damaged or even loose Ethernet and coaxial cables can cause major slow downs and interruptions. Your cables may not be connected probably or damaged from excess stress, kinks, or even chewing from pets. 5. You need to update your devices It’s not always your internet connection that’s causing the slowdowns, it could be one or more of your devices. If your slowdowns are limited to certain devices, you should start your troubleshooting efforts with those devices rather than your internet connection; sometimes, they just need a simple restart or an update. 6. You have high latency High latency causes your internet to feel sluggish and is particularly frustrating with highly time-sensitive activities like gaming and video calls. 7. Your provider’s network is congested Provider networks can get overloaded the same way your home network can: too much traffic and not enough bandwidth. 8. Your provider is throttling your connection Your ISP may be intentionally slowing down your connection for a number of reasons. How Much Internet Speed Do I Need?Est. Time: 60 seconds Answer 6 questions and get a personalized internet speed recommendation! How many people in your household use the internet/WiFi on a daily basis? How many devices in your home connect to the internet, including tablets, gaming consoles, and smart devices? How many people in your household work from home? What video quality do you use for streaming TV and movies? How intensely does your household participate in online gaming? Does your household download large files from the cloud or via the internet? Our minimum speed recommendation for you: How to fix a slow internet connection1. you need to restart your modem and router. As the golden rule of internet troubleshooting, an equipment restart should always be your first step. It’s quick, easy, and effective. The restart process is the same for a modem, router, or gateway (modem/router combo unit): Step 1: Unplug the power cable from the back of the modem, router, or gateway. Step 2: Wait 60 seconds. Step 3: Plug the power cable back into the back of the equipment. Step 4: Wait for the equipment to reboot (this can take up to 20 minutes). 2. Your home network is congestedYour slow speeds might be the result of trying to do too much at once on your internet connection. Think of your internet connection as a road directly to your house. One car’s worth of people (or internet data) can reach your house at a time. If there are three cars trying to get there, they have to line up to get to your house. And if more cars arrive as the others are waiting to reach your house, you get a traffic jam. Here’s how you can tell if you need to upgrade your internet plan: Use our internet speed test to see if you’re getting the speed advertised by your ISP. If your results are close to your plan speed, consider upgrading. Download speed 000 Mbps Upload speed 000 Mbps Latency (ping) 00 ms Jitter 00 ms  You can also fix home network congestion by dialing back your internet usage. Thankfully, there are severa l easy ways to do this that don’t include yelling at everyone to get off the internet so you can attend a Zoom meeting. Here are a few tips on how to manage your home network traffic: Use QoS settings to prioritize certain online activitiesMany routers have a quality of service (or QoS) component that allows you to prioritize certain types of traffic on your home network. For example, you can make sure your streaming data always gets first access to available bandwidth for smooth playback. Not all routers have adjustable QoS, but if your router does, you’ll find the controls in your router’s web interface. If you need help accessing your router’s settings see our guide on how log into your router . Prune your internet connectionsThere may be some devices connected to your network that you rarely use—if at all. Even if you’re not actively using these devices, it still uses bandwidth for updates and other background services. Your router may even have a limited number of devices it can connect to simultaneously, and start kicking some of them off the network when you go over the limit. One simple way to take stock of all the devices using your network is to load your router’s web interface and view the network map. You will see all connected devices, whether they’re active or not, so you can block the ones you never use. Some routers have an app you can use instead of a web interface. Another method is to change the Wi-Fi password, but that only applies to wireless devices . Once you do , you must manually reconnect every device . Stagger bandwidth-hogging activitiesIf your connection can’t handle everyone online at once, stagger your internet activities so everyone gets a chance at an uninterrupted connection. Also, make sure to schedule big downloads (like computer and game updates) during times when other people won’t be online. Put visitors on a guest networkYou can create a second guest network using your router’s web interface or mobile app. A guest network allows you to limit how much bandwidth guests can use, and what services and websites they can access . It also provides improved security by preventing guests’ devices from mingling with your devices, so there’s no worry about guests spreading malware to everything you use. Our guide on how to set up guest Wi-Fi covers a few different ways to establish a second network. 3. You need a stronger Wi-Fi signalWalls, distance, and interference from other Wi-Fi networks can weaken your Wi-Fi signal. Weaker Wi-Fi signals mean slower speeds and frequent disconnects . You can tell if signal interference and weak Wi-Fi signals are your issue by looking at your devices Wi-Fi meter . For fast connection, we recommend ensuring you have at least three bars of signal strength. To fix weak Wi-Fi, first, check your router’s placement. Y ou want to make sure your router is in a central and elevated location and away from things that can affect your Wi-Fi signals (like walls, Bluetooth speakers, etc.). Sometimes, even moving your router a few feet can make a big difference. See our guide on choosing the best spot for your router . We also have a walkthrough on how to move your router to another room , which may be required to get adequate Wi-Fi coverage throughout your home. If that doesn’t work, you might need to replace your router with one designed for longer ranges or better coverage—or you can add an extender to your network to stretch Wi-Fi signals into a previously unreachable area . Check out our guides on how to extend your Wi-Fi range and long-range routers if you need better Wi-Fi coverage. 4. Your networking cables are loose or damagedLoose or damaged networking cables can degrade your internet signal, introduce signal interference, or even cutoff your bandwidth altogether. The first step to make sure everything is connected properly. Start with your Ethernet cables, which look like and oversized phone line and are used to connect devices directly to your router and connect your router to your modem (unless you have an internet gateway, which is both a modem and a router). Check that the cable is fully inserted in the sockets on the modem, router, and any devices connected directly to your router; it should make an audible click when it plugged in; if it doesn’t, the plastic spring clip is worn and the cable should be replaced. Also, check for any kinks, tears, chew marks, or any other obvious sign of wear and tear. If you see damage, replace the cable, there’s no fixing it. If you have an internet gateway instead of a modem and router and you use Wi-Fi for all your devices, it’s possible you’re not even using any Ethernet cables in your home network. Next, check the cable that delivers internet signal to your modem or gateway. If you have cable internet, it will be a coaxial cable. If you have fiber, it could be a fiber-optic cable or Ethernet cable. Check that the coaxial cable is screwed on hand-tight to the back of the modem or gateway. And again, look for any signs of damage; if you spot damage, you need to replace the cable. 5. You have high latencyLatency is the time data takes to make a round trip from your device to the destination and back. A high latency creates noticeable lag: an extended duration between your physical actions and the results displayed on your screen. This can be particularly frustrating with online gaming or video calls. High latency is difficult to work around. It depends partially on your physical distance from internet servers, network congestion between you and the servers , and your internet provider’s infrastructure—things that are mostly beyond your control. Internet type can also play into latency as well. For example, satellite internet has high latency because all your data must travel to space and back, both coming and going to your device. Newer types of internet, including fiber and 5G mmWave , have lower latency because they can handle faster signals. If you’re looking to lower your latency for a better connection, check out our report on the fastest ISPs . It dives into which internet services have the best tested speeds and lowest average latency. 6. Your devices need an update or are outdatedThe problem might not be with your internet connection—it might be with the device you use . Your computer, tablet, phone, or gaming console could need an update or be too old to process today’s Wi-Fi speeds. For example, the old (but much loved) PlayStation Vita handheld console supports up to 150 Mbps per second because it uses a Wi-Fi 4 radio. That speed can decrease based on the router it connects to and the security protocol it uses. The Vita will never see speeds beyond that 150 Mbps limit. If you have speed issues on a desktop or laptop, make sure you have the latest OS and networking updates. Then, try power cycling the device. This clears the memory of any junk, refreshes your connection, and cleans out unnecessary processes and temporary files. Speed issues tend to happen due to an overworked processor, and a quick power cycle—shutting it down completely for 30 seconds—will “clear its head.” Other things that can slow down your devices include the following:
Avoid overwhelming your computer’s CPU by closing unused applications and browser windows. Keep your device’s operating system up to date by allowing auto-updates, and keep your antivirus definitions current. 7. Your provider’s network is congestedYour ISP is also susceptible to network congestion. It’s similar to congestion on your home network but on a larger scale. If the congestion gets particularly bad, your internet provider may throttle internet speeds in your area to reduce traffic for the network. Unfortunately, large-scale network congestion is out of your control, but you can try to work around it by s cheduling big downloads during non-peak hours, like in the middle of the night. When dealing with heavy ISP slowdowns that don’t resolve, the only real fix is switch ISPs. Luckily, there are lots of new services available, like 5G home internet, Satellite, and new fiber developments. If you’re craving a shiny new ISP, run your zip code in the search bar below; chances are you have some new ISP options. 8. ISP throttlingInternet providers can throttle your speeds, causing a slow connection . We’ll go over throttling briefly here, but you can get a more in-depth look at the subject in our guide to network throttling . We’ve already discussed a few circumstances where a provider might throttle your speeds—like if you go over your data cap or if there’s too much congestion in the network. But your provider might also slow you down if it flags your internet activity as potentially illegal or if it generally doesn’t want you to do a specific type of activity (like torrenting). To see if your provider is throttling your internet, run a speed test normally and then run it again using a VPN. If your speeds improve with the VPN, congratulations! You’re throttled. Other factors that affect your speedYour internet plan’s maximum speed. Internet speeds are measured in megabits per second (Mbps) . This refers to your connection’s total bandwidth, not the actual time data uses to make a round trip to a website and back—that’s called latency. Providers usually advertise their internet speeds as “up to” a certain number of megabits per second, and there’s usually some fine print that says those speeds are not guaranteed. Internet providers are mostly in the clear legally if your internet doesn’t actually perform up to the highest advertised bandwidth. Realistically, you may pay for 400 Mbps per month, but you may not see that maximum due to hardware issues between your internet provider’s operator—a device that communicates with multiple modems—and your physical internet connection. Utility pole connections, your buried cable, and so on all play a major factor in how your connection performs. If you need a refresher on internet speeds and what they mean, check out our guide to internet speeds . Your upload and download speedsYou upload and download data every day, whether you’re on a smartphone or a laptop. For instance, when you access a website, you upload a request to that website and then download temporary files from the site to view it in your browser. If you don’t have issues with streaming on Netflix or downloading files but are still experiencing some symptoms of slow internet speeds, your issue might actually be with your upload speed. Cable, DSL, and satellite providers give customers way less upload bandwidth than download bandwidth because most people request much more information from the internet than they send. Upload speed is typically an issue for heavy uploaders—like Twitch streamers , people who work with video or audio , or those who often have to share large files. The best way to improve upload speeds is to switch to a fiber plan. Fiber-optic internet connections often give customers upload speeds equal to their download speeds. If you don’t know what kind of speeds you really need , check out our recommendations for upload and download speeds . Your internet connection typeThere are a few different technologies internet providers use to deliver your connection, like cable, fiber, satellite, or DSL. Your internet connection type p lays a huge factor in your overall speeds. Satellite internet transfers internet signals from a base station to a satellite to a receiver at your home. Because all your information must travel such a long distance both ways, satellite internet can have very high latency compared to other types of internet, which slows things down. DSL internet uses phone lines to carry data. It can’t handle the same amount of bandwidth as cable or fiber. DSL internet tops out at just over 100 Mbps, and its electrical signals tend to degrade in quality over long distances. Cable internet is faster than DSL because it uses coaxial cables that have a higher bandwidth than phone cables . Speeds can reach up to 1,200 Mbps. Fiber-optic internet is one of the newest types of internet, and it’s the best wired connection you can get. Fiber uses light pulses to send your internet data, so it has lower latency than other internet types as a whole. It can also carry much more bandwidth than cable or DSL, offering speeds up to 5 ,000 Mbps. It’s less prone to network congestion and offers equally high download and upload speeds. Overall, DSL and cable are the most common internet types while fiber is newer but scarce. Satellite is best for rural areas where the other three types can’t reach. More ways to speed up a slow internet connectionWe provide some quick tips below to help speed up your internet connection. But if you’re ready to get to the bottom of your internet speed issues with some thorough troubleshooting, see our internet troubleshooting guide . First, know your plan speedYou need to know how much speed you pay for each month and compare that number against the speed you’re actually getting now . Look on your paper bill or log in to your online account to see your plan’s advertised maximum speed. Next, run a speed test and compareRunning a series of speed tests while connected to different points in your network can help you figure out where your speeds are slowing down. We’ll break the testing process down into two sections. Part 1: Test the modem Your first speed test is to see if you’re getting the correct speeds to your home compared with what you’re supposed to get from your internet provider . To get the most accurate results for your initial speed test, unplug your router from the modem and connect a computer to the same port on the modem using an Ethernet cable. If you have a wireless gateway, just plug it into one of the Ethernet ports. Warning: We don’t recommend browsing the internet for extended periods of time without using a router. Your router has some excellent built-in security features that protect your network from viruses and malware. This first test should give you results that are close to the speeds promoted with your plan. If not, try to track this issue over multiple days and times of day to establish a pattern. Contact your internet provider to talk about why you’re not getting the correct speeds if you continue to see lower than expected results .  Part 2: Test the router If your modem isn’t the issue, the next step is to test the router. Plug the router back into the modem and run multiple speed tests using your wireless devices, and wired devices plugged into the router’s Ethernet ports. If you see a vast difference between the modem and router tests, then your router is causing your connection slowdowns—or the Ethernet cable tethering your router to the modem. Keep in mind that not all wireless devices experience identical speeds. Their connections depend on the hardware inside no matter what router you use, so a budget Samsung phone will have slower Wi-Fi speeds than an expensive wireless card plugged into your desktop. To troubleshoot router problems, follow these steps: Step 1: Unplug the router’s power , wait 30 seconds, and then plug it back in. Step 2: Make sure all cables are connected securely and that all ports work. Step 3: Update your router’s firmware. You can do this by logging in to your router’s web interface or mobile app . (Your ISP likely does this automatically, but it’s worth checking.) Step 4: Reposition your router . Step 5: Move wireless connections to the best Wi-Fi band . Step 6: Change Wi-Fi channels in your router’s interface to find one that’s less crowded. Step 7: Try a factory reset by pressing the reset button located on the back of your router. If none of these steps work, you may need to upgrade to a newer or more powerful router. Internet tech advances rather quickly, and if your router is more than a few years old, it might be time to get yourself something more modern . If you’re looking for router-buying guidance, we have recommendations for the best long-range routers , the best modem and router combos , and the best routers for Xfinity . Check for Wi-Fi dead zonesWi-Fi problems can stem from multiple factors . It could be your router’s range, a crowded frequency channel or band, or signal interference caused by physical obstructions and other electronics. You already know that you should place your router at a central and elevated location for the best coverage, so we’ll assume that you’ve already done that and pointed your antennas in the right direction. Go to different areas of your house with a computer or smartphone and watch the Wi-Fi signal strength indicator. If you notice a lot of dead zones, you may need to move your router again (if they happen in areas where you normally need Wi-Fi) or invest in something to boost your Wi-Fi signal to that particular area. You can also make a Wi-Fi heatmap if you want to get more precise with it. If you have more than a couple of issues with Wi-Fi dead zones, we recommend upgrading to a mesh networking kit . They usually ship with at least two nodes—one that connects to your modem and another that communicates directly with the first unit—to create a ”blanket” of coverage. There’s no centralized point, and you can easily add more nodes to extend coverage. Moreover, devices seamlessly switch between nodes as you move about the home or office. If you prefer to stick with the traditional router, you could add a Wi-Fi extender or powerline adapter , However, we still prefer mesh router kits versus the router/extender setup . Reorganize your Wi-Fi connectionsIf you’ve already pruned your Wi-Fi connections of unnecessary devices , it’s time to make sure all active connections are on the correct Wi-Fi band. Most modern routers offer two Wi-Fi bands, which each create their own visible Wi-Fi network. By default, these are usually labeled with their frequency bands, but it might be different if you’ve changed your Wi-Fi network’s name. These bands operate on two different frequencies: 2.4 GHz and 5 GHz. The 2.4 GHz frequency band has a better range, but it’s slower and more susceptible to signal interference from other electronics. The 5 GHz band is faster but can’t travel as far. Basically, you want to use the 5 GHz band for most bandwidth-heavy applications like streaming or gaming. Devices that don’t need that much speed—like smart home devices— should use the 2.4 GHz band instead . Typically, you can change the Wi-Fi band each device uses by logging in to the correct Wi-Fi network on each device. However, some routers broadcast only one network name and automatically selects the best frequency band for your device. This can be problematic if you really need the faster 5 GHz connection, but the router forces your device to use the 2.4 GHz band. Change your Wi-Fi band’s channelChanging your router’s channel is a standard troubleshooting suggestion, but it may not work, and here’s why. All three frequency bands are divided into small 20 MHz channels, and routers combine these channels to make larger ones. Most modern Wi-Fi 5 and Wi-Fi 6 devices use 80 MHz channels when they connect to the 5 GHz band for the most speed, so routers use these by default. The thing is, routers only list the smaller channels, so you may run a Wi-Fi diagnostics app and see that channel 36 is clear for you to use, but in reality, it’s probably being used by a neighboring network that, like yours, combines channels 36, 40, 44, and 48 to create one 80 MHz channel. If that’s the case, your best bet is to select one of the higher 5 GHz channels (if they’re available to you) and hope for the best. Most standalone routers allow you to change the channel in the web interface or mobile app, but you usually can’t change the channel on a mesh system. Check connected devicesAs we mentioned before, sometimes the issue isn’t with your internet connection— it’s with the smartphone, computer, or tablet you’re using to access the internet . It may need a reboot, it may be outdated, or you have too many apps and programs open, bogging down the device’s processor. Manage your networkIf you’ve made it this far and you’re still experiencing problems with slow internet speeds, run through the tips in the home network traffic section of this post if you haven’t already. Your speed issues most likely stem from your internet provider’s reliability or the traffic on your own home network. Even if you’ve organized and trimmed down your number of connected devices, you could still not have enough bandwidth at certain times of day to cover everything your network has to handle. The only solution to this is to either use the internet less or get a faster internet plan. Check out every provider and plan in your area to see if you can get better speeds for a better deal. Quick fixes for slow internet speeds (and why they work)Before we dive in, download our internet speed test. Measuring your internet speed and knowing how it compares to the speeds you pay for is an important part of diagnosing a slow connection. Fix #1: Power cycle your modem and router (or wireless gateway)Your modem and router work hard , and sometimes they need to refresh with a quick power cycle. Simply pull the plug on both units, wait 30 seconds, and then plug the modem back into the wall outlet. Once it properly boots, do the same with the router. In the case of a wireless gateway, pull the plug, wait, and plug it back in. Draining both units of power allows them to clear the system memory, clear up any local communication issues, and reestablish fresh connections. Moreover, a power cycle allows the modem to resync with your internet provider’s operator—a device that communicates with multiple modems. It also refreshes your router’s public IP address. Overall, a power cycle can really give your internet speeds a boost on your side of the modem. Fix #2: Move your router to another locationMany people hide their routers or wireless gateways in closets, behind furniture , or down in basement s . Don’t be one of those people unless you want excessively bad Wi-Fi. Instead , put as few physical barriers between your router and your devices as possible. Walls, floors, ceilings , doors, large furniture, and similar obstructions can barricade your Wi-Fi signals and reduce connection speeds , especially over longer distances. Certain signals from other devices can also interfere with your wireless speeds. These include microwaves, Bluetooth speakers, baby monitors, and cordless phones. For the best Wi-Fi coverage, place your router in a central, elevated location, or at a location where you use Wi-Fi the most, like in a home office . Be sure to use your router’s external antennas ( if present ) to get better Wi-Fi coverage. Most router antennas broadcast Wi-Fi signals in an outward circle perpendicular to the antenna’s position . For instance, if the antennas are positioned vertically, the Wi-Fi signals broadcast horizontally in all directions. That said, if you live in a one-story house, keep the antennas vertical. If you live in a multistory house, position at least one antenna horizontally so the Wi-Fi signals reach the additional floors. Fix #3: Use the internet during off-peak hoursIf you know there’s a big download in your future— the latest version of macOS or a 100 GB update for an Xbox Series X game—you might want to schedule a time when you don’t need to do anything else online. The early morning hours are ideal when everyone is asleep and no other downloads currently hog your bandwidth. Operating systems tend to wait until the early morning hours when you’re fast asleep. Game updates, meanwhile, typically require you to manually start the download. Other updates aren’t quite so accommodating with your schedule. If your internet gets too slow to stream during certain peak hours, download the content earlier in the day (or again, in the middle of the night) so you’ll be ready to binge watch all of Avatar: The Last Airbender without buffering -related interruptions. Fix #4: Upgrade your internet planYou may need a faster plan if more people live with you now, if you transitioned to working from home, or if you generally use the internet more than you did before. Enter your zip code below to find a speedier plan that’s available in your area . How do I know if I need a faster internet plan?What is type of internet plan is the fastest. Fiber internet is the fastest type of internet connection you can get. Many residential fiber-optic internet plans offer speeds up to 5,000 Mbps. There are even some fiber plans that offer 10,000 Mbps of bandwidth. Additionally, fiber internet offers symmetrical speeds, meaning your upload speeds are just as fast as your download speeds—a handy feature for activities like zoom calls, twitch streaming, and uploading large files. Read page in Spanish Author - Austin Aguirre Austin worked as a broadband technician installing and troubleshooting countless home internet networks for some of the largest ISPs in the U.S. He became a freelance writer in 2020 specializing in software guides. After graduating with a BS in technical communication from Arizona State University, he joined the team at HighSpeedInternet.com where he focuses on home network improvement and troubleshooting. Editor - Cara Haynes Cara Haynes has been editing and writing in the digital space for seven years, and she's edited all things internet for HighSpeedInternet.com for five years. She graduated with a BA in English and a minor in editing from Brigham Young University. When she's not editing, she makes tech accessible through her freelance writing for brands like Pluralsight. She believes no one should feel lost in internet land and that a good internet connection significantly extends your life span. 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Problem 8: A man walked from point A to F following the route in the grid below in 3250 seconds. Determine. a) the average speed, in m/s, for the whole journey. b) the magnitude of the displacement. c) the magnitude of the average velocity, in m/s, for the whole journey. Solution to Problem 8.
Problem 5: If I can walk at an average speed of 5 km/h, how many miles I can walk in two hours? Solution to Problem 5: distance = (average speed) * (time) = 5 km/h * 2 hours = 10 km using the rate of conversion 0.62 miles per km, the distance in miles is given by distance = 10 km * 0.62 miles/km = 6.2 miles Problem 6: A train travels along a straight line at a constant speed of 60 mi/h for a ...
Distance, rate and time problems are a standard application of linear equations. When solving these problems, use the relationship rate (speed or velocity) times time equals distance. r⋅t = d r ⋅ t = d. For example, suppose a person were to travel 30 km/h for 4 h. To find the total distance, multiply rate times time or (30km/h) (4h) = 120 km.
speed = ? and the formula for speed. speed = distance/time = 5000/50 = 100m/s . Problem 3. A motorcycle starting from rest moves with a uniform acceleration until it attains a speed of 108 kilometres per hour after 15 seconds. Find its acceleration. Solution. Data:
Here we will learn to solve different types of problems on calculating speed. We know, the speed of a moving body is the distance traveled by it in unit time. Formula to find out speed = distance/time. Word problems on calculating speed: 1. A man walks 20 km in 4 hours. Find his speed. Solution: Distance covered = 20 km
This speed problem better makes it clear to us the difference between average speed and average speed. ... {align*} By reorganizing this expression, we obtain a formula that is useful for solving similar problems in the AP Physics 1 exams. \[\text{average speed}=\frac{2v_{up} \times v_{down}}{v_{up}+v_{down}}\] Substituting the numerical values ...
Average speed is a scalar, so we do not include direction in the answer. We can check the reasonableness of the answer by estimating: 5 meters divided by 2 seconds is 2.5 m/s. Since 2.5 m/s is close to 2.9 m/s, the answer is reasonable. This is about the speed of a brisk walk, so it also makes sense.
Make customizable worksheets about constant (or average) speed, time, and distance for pre-algebra and algebra 1 courses (grades 6-9). Both PDF and html formats are available. You can choose the types of word problems in the worksheet, the number of problems, metric or customary units, the way time is expressed (hours/minutes, fractional hours, or decimal hours), and the amount of workspace ...
Time problem. We can solve problems involving time by remembering the formula for speed, distance and time. E.g. Calculate the time if a car travels at 15 miles at a speed of 36 mph. Time = distance ÷ speed. Time = 15 ÷ 36 = 0.42 hours. 0.42 60 = 25.2 minutes. E.g. A train travels 42km between two stops at an average speed of 36 km/h.
Examples on Speed Formula. Let us solve some interesting problems using the speed formula. Example 1: A train covered a distance of 120 km in an hour. Determine the speed of the train in m/s using the speed formula. Solution: To find: The speed of the train.
If they take 6 minutes then they averaged 1 unit of length per minute, this is their average speed (usually taken to just be speed). On the other hand, velocity depends on a distance (called displacement) and ' direction. If A walks around the block (4 equal sides), she may have walked 4 units of length in 4 minutes; giving her a speed of 1 ...
Solving for time. Displacement from time and velocity example. Instantaneous speed and velocity. Acceleration: At a glance. ... Problem. A car travels from point A to B in 3 hours and returns back to point A in 5 hours. ... The average speed is 37.5 miles per hour. C. The average speed is 37.5 miles per hour. (Choice D)
Solution: Step 1: The formula for distance is. Distance = Rate × Time. Total distance = 50 × 3 + 60 × 2 = 270. Step 2: Total time = 3 + 2 = 5. Step 3: Using the formula: Answer: The average speed is 54 miles per hour. Be careful! You will get the wrong answer if you add the two speeds and divide the answer by two.
speed = distance/time. To solve for time use the formula for time, t = d/s which means time equals distance divided by speed. time = distance/speed. Time Entry Formats hh:mm:ss. You can use a dash (-), period (.) or colon (:) as separators and must always use 2 separators. For example, 15-06-22, 15.06.22 and 15:06:22 are all interpreted as 15 ...
The formula to find time is. Time taken to cover 330 miles distance at the speed of 60 miles per hour is. = ³³⁰⁄₆₀. = 5.5 hours. = 5 hrs 30 minutes. So, if the person is increased by 50%, it will take 5 hrs 30 minutes to cover 330 miles distance. Problem 10 : A person speed at a rate of 40 kms per hour.
The Corbettmaths Practice Questions on Speed, Distance, Time
Rate is distance per time, so its units could be mph, meters per second, or inches per year. Now you can solve the system of equations: 50t = 100 (t - 2) (Multiply both values inside the parentheses by 100.) 50t = 100t - 200. 200 = 50t (Divide 200 by 50 to solve for t.) t = 4. Substitute t = 4 into train No. 1.
Xcelerate Math resources https://xceleratemath.com/number/speedTime stamps⏰00:00 Introduction00:20 DST triangle01:19 Question 1: Find the distance (fast car)...
The examples so far calculate average speed: how far something travels over a period of time. But speed can change as time goes by. A car can go faster and slower, maybe even stop at lights. So there is also instantaneous speed: the speed at an instant in time. We can try to measure it by using a very short span of time (the shorter the better).
Solution: Distance traveled = 25 km. Time taken to travel = 6 hours. Speed of Man = Distance traveled/Time taken. = 25km/6hr. = 4.16 km/hr. Therefore, a man travels at a speed of 4.16 km/hr. 2. A car covers a distance of 420 m in 1 minute whereas a train covers 70 km in 30 minutes.
Time = Distance / Speed. Let us take a look at some simple examples of distance, time and speed problems. Example 1. A boy walks at a speed of 4 kmph. How much time does he take to walk a distance of 20 km? Solution. Time = Distance / speed = 20/4 = 5 hours. Example 2. A cyclist covers a distance of 15 miles in 2 hours.
average speed = s/t = 88/20 = 4,4 m/s (b) in one complete revolution displacement of car is zero. v avr = displacement/time = 0/10 = 0 m/s Problem #5 a train travels from city A to city B with a constant speed of 20 ms-1 and return back to city A with a constant speed of 30 m.s-1. Find its average speed during te entire journey. Answer:
Speed Boat #gamestorming #problem solving #action . Speedboat is a short and sweet way to identify what your employees or clients don't like about your product/service or what's standing in the way of a desired goal. 17. The Journalistic Six.
Semiconductors at scale: New processor achieves remarkable speedup in problem solving. Annealing processors are designed specifically for addressing combinatorial optimization problems, where the ...
It's quick, easy, and effective. The restart process is the same for a modem, router, or gateway (modem/router combo unit): Step 1: Unplug the power cable from the back of the modem, router, or gateway. Step 2: Wait 60 seconds. Step 3: Plug the power cable back into the back of the equipment.