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Time and Work Formula and Solved Problems

The basic formula for solving is: 1/r + 1/s = 1/h
Let us take a case, say a person Hrithik
Let us say that in 1 day Hrithik will do 1/20 th of the work and 1 day Dhoni will do 1/30 th of the work. Now if they are working together they will be doing 1/20 + 1/30 = 5/60 = 1/12 th of the work in 1 day. Now try to analyze, if two persons are doing 1/12 th of the work on first day, they will do 1/12 th of the work on second day, 1/12 th of the work on third day and so on. Now adding all that when they would have worked for 12 days 12/12 = 1 i.e. the whole work would have been over. Thus the concept works in direct as well as in reverse condition.
The conclusion of the concept is if a person does a work in ‘r’ days, then in 1 day- 1/r th of the work is done and if 1/s th of the work is done in 1 day, then the work will be finished in ‘s’ days. Thus working together both can finish 1/h (1/r + 1/s = 1/h) work in 1 day & this complete the task in ’h’ hours.
The same can also be interpreted in another manner i.e. If one person does a piece of work in x days and another person does it in y days. Then together they can finish that work in xy/(x+y) days
In case of three persons taking x, y and z days respectively, They can finish the work together in xyz/(xy + yz + xz) days

Time and work problems

Time and work concepts, time and work problems (easy), time and work problems (difficult), most popular articles - ps.

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Government Exam Articles
Time and Work - Concept, Formula & Aptitude Questions

Time and Work - Concept, Formula & Aptitude Questions

Time and Work is one of the most common quantitative aptitude topics which is asked in the Government exams . This is one of those topics which candidates are familiar with even before they start their competitive exam preparation.

The concept of time and work remains the same, however, the type of questions asked may have a bit of variety. Mostly, 1-2 words problems are asked from this topic but candidates must also keep themselves prepared to have questions in data sufficiency and data interpretation to be picked up from time and work.

Candidates can check the detailed syllabus for the quantitative aptitude section along with the list of exams, which include this subject as a part of its syllabus and can visit the linked article.

For aspirants who shall be appearing for the competitive exams for the first time or the ones who are preparing for the exams for a while must know that sufficient time must be devoted to each subject so that your concept and basics are clear. This will help you cope with the tough competition for each exam.

In this article, we bring to you the concept of time and work along with the formulas which shall help you answer the questions easily. Also, further below in the article, we have a few sample time and work questions with solutions for your reference.

Interested aspirants can also check the links given below and strengthen their preparation for the quantitative aptitude section:

Time and Work Questions PDF:- Download PDF Here

Time and Work – Introduction and Concept

Before we move on to the questions and important formulas, it is important that a candidate is well aware of the concept and the types of questions which may be asked in the exam.

Time and work deals with the time taken by an individual or a group of individuals to complete a piece of work and the efficiency of the work done by each of them.

Time and Work - Quantitative Aptitude for Government Exams

Given below are the basic type of questions which may be asked in the exam with respect to the time and work topic:

To find the efficiency of a person
To find the time taken by an individual to do a piece of work
To find the time taken by a group of individuals to complete a piece of work
Work done by an individual in a certain time duration
Work done by a group of individuals in a certain time duration

Mostly the questions asked may involve one of these things to find and candidates can use the related formulas to easily get through the answers for the same.

A few other quantitative aptitude related links have been given below. It is suggested that candidates go through each of these topics carefully to excel in the upcoming Government exams:

Important Time and Work Formula

Knowing the formulas can completely link you to a solution as soon as you read the question. Thus, knowing the formula for any numerical ability topic make the solution and the related calculations simpler.

Given below are a few such important time and work formulas for your reference:

Work Done = Time Taken × Rate of Work
Rate of Work = 1 / Time Taken
Time Taken = 1 / Rate of Work
If a piece of work is done in x number of days, then the work done in one day = 1/x
Total Wok Done = Number of Days × Efficiency
Efficiency and Time are inversely proportional to each other
X:y is the ratio of the number of men which are required to complete a piece of work, then the ratio of the time taken by them to complete the work will be y:x
If x number of people can do W1 work, in D1 days, working T1 hours each day and the number of people can do W2 work, in D2 days, working T2 hours each day, then the relation between them will be

Aspirants for the various Government exams must start their preparation now to ensure they give their 100 per cent and complete hard work and dedication to their preparation.

Time & Work – Sample Questions

All the hard work can go in vain if the candidate does not solve questions based on time and work on a regular basis and try using the different formulas to crack the solution for each question in an even shorter time span.

So, discussed below are a few time and work questions to give an idea as to what type of questions are asked in the competitive exam and what format and pattern is used for the same.

Q 1. A builder appoints three construction workers Akash, Sunil and Rakesh on one of his sites. They take 20, 30 and 60 days respectively to do a piece of work. How many days will it take Akash to complete the entire work if he is assisted by Sunil and Rakesh every third day?

Answer: (2) 15 days

Total work done by Akash, Sunil and Rakesh in 1 day = {(1/20) + (1/30) + (1/60)} = 1/10

Work done along by Akash in 2 days = (1/20) × 2 = 1/10

Work Done in 3 days (1 day of all three together + 2 days of Akash’s work) = (1/10) + (1/10) = 1/5

So, work done in 3 days = 1/5

Time taken to complete the work = 5×3 = 15 days

Q 2. To complete a piece of work, Samir takes 6 days and Tanvir takes 8 days alone respectively. Samir and Tanvir took Rs.2400 to do this work. When Amir joined them, the work was done in 3 days. What amount was paid to Amir?

Answer: (1) Rs.300

Total work done by Samir and Tanvir = {(1/6) + (1/8)} = 7/24

Work done by Amir in 1 day = (1/3) – (7/24) = 1/24

Amount distributed between each of them = (1/6) : (1/8) : (1/24) = 4:3:1

Amount paid to Amir = (1/24) × 3 × 2400 = Rs.300

Q 3. Dev completed the school project in 20 days. How many days will Arun take to complete the same work if he is 25% more efficient than Dev?

Answer: (3) 16 days

Let the days taken by Arun to complete the work be x

The ratio of time taken by Arun and Dev = 125:100 = 5:4

5:4 :: 20:x

⇒ x = {(4×20) / 5}

Q 4. Time taken by A to finish a piece of work is twice the time taken B and thrice the time taken by C. If all three of them work together, it takes them 2 days to complete the entire work. How much work was done by B alone?

Cannot be determined

Answer: (2) 6 days

Time taken by A = x days

Time taken by B = x/2 days

Time Taken by C = x/3 days

⇒ {(1/x) + (2/x) + (3/x) = 1/2

⇒ 6/x = 1/2

Time taken by B = x/2 = 12/2 = 6 days

Q 5. Sonal and Preeti started working on a project and they can complete the project in 30 days. Sonal worked for 16 days and Preeti completed the remaining work in 44 days. How many days would Preeti have taken to complete the entire project all by herself?

Answer: (5) 60 days

Let the work done by Sonal in 1 day be x

Let the work done by Preeti in 1 day be y

Then, x+y = 1/30 ——— (1)

⇒ 16x + 44y = 1 ——— (2)

Solving equation (1) and (2),

Thus, Preeti can complete the entire work in 60 days

Candidates must solve more such questions to understand the concept better and analyse the previous year papers to know more about the pattern of questions asked.

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Chapter 9: Radicals

9.10 Rate Word Problems: Work and Time

If it takes Felicia 4 hours to paint a room and her daughter Katy 12 hours to paint the same room, then working together, they could paint the room in 3 hours. The equation used to solve problems of this type is one of reciprocals. It is derived as follows:

[latex]\text{rate}\times \text{time}=\text{work done}[/latex]

For this problem:

[latex]\begin{array}{rrrl} \text{Felicia's rate: }&F_{\text{rate}}\times 4 \text{ h}&=&1\text{ room} \\ \\ \text{Katy's rate: }&K_{\text{rate}}\times 12 \text{ h}&=&1\text{ room} \\ \\ \text{Isolating for their rates: }&F&=&\dfrac{1}{4}\text{ h and }K = \dfrac{1}{12}\text{ h} \end{array}[/latex]

To make this into a solvable equation, find the total time [latex](T)[/latex] needed for Felicia and Katy to paint the room. This time is the sum of the rates of Felicia and Katy, or:

[latex]\begin{array}{rcrl} \text{Total time: } &T \left(\dfrac{1}{4}\text{ h}+\dfrac{1}{12}\text{ h}\right)&=&1\text{ room} \\ \\ \text{This can also be written as: }&\dfrac{1}{4}\text{ h}+\dfrac{1}{12}\text{ h}&=&\dfrac{1 \text{ room}}{T} \\ \\ \text{Solving this yields:}&0.25+0.083&=&\dfrac{1 \text{ room}}{T} \\ \\ &0.333&=&\dfrac{1 \text{ room}}{T} \\ \\ &t&=&\dfrac{1}{0.333}\text{ or }\dfrac{3\text{ h}}{\text{room}} \end{array}[/latex]

Example 9.10.1

Karl can clean a room in 3 hours. If his little sister Kyra helps, they can clean it in 2.4 hours. How long would it take Kyra to do the job alone?

The equation to solve is:

[latex]\begin{array}{rrrrl} \dfrac{1}{3}\text{ h}&+&\dfrac{1}{K}&=&\dfrac{1}{2.4}\text{ h} \\ \\ &&\dfrac{1}{K}&=&\dfrac{1}{2.4}\text{ h}-\dfrac{1}{3}\text{ h}\\ \\ &&\dfrac{1}{K}&=&0.0833\text{ or }K=12\text{ h} \end{array}[/latex]

Example 9.10.2

Doug takes twice as long as Becky to complete a project. Together they can complete the project in 10 hours. How long will it take each of them to complete the project alone?

[latex]\begin{array}{rrl} \dfrac{1}{R}+\dfrac{1}{2R}&=&\dfrac{1}{10}\text{ h,} \\ \text{where Doug's rate (} \dfrac{1}{D}\text{)}& =& \dfrac{1}{2}\times \text{ Becky's (}\dfrac{1}{R}\text{) rate.} \\ \\ \text{Sum the rates: }\dfrac{1}{R}+\dfrac{1}{2R}&=&\dfrac{2}{2R} + \dfrac{1}{2R} = \dfrac{3}{2R} \\ \\ \text{Solve for R: }\dfrac{3}{2R}&=&\dfrac{1}{10}\text{ h} \\ \text{which means }\dfrac{1}{R}&=&\dfrac{1}{10}\times\dfrac{2}{3}\text{ h} \\ \text{so }\dfrac{1}{R}& =& \dfrac{2}{30} \\ \text{ or }R &= &\dfrac{30}{2} \end{array}[/latex]

This means that the time it takes Becky to complete the project alone is [latex]15\text{ h}[/latex].

Since it takes Doug twice as long as Becky, the time for Doug is [latex]30\text{ h}[/latex].

Example 9.10.3

Joey can build a large shed in 10 days less than Cosmo can. If they built it together, it would take them 12 days. How long would it take each of them working alone?

[latex]\begin{array}{rl} \text{The equation to solve:}& \dfrac{1}{(C-10)}+\dfrac{1}{C}=\dfrac{1}{12}, \text{ where }J=C-10 \\ \\ \text{Multiply each term by the LCD:}&(C-10)(C)(12) \\ \\ \text{This leaves}&12C+12(C-10)=C(C-10) \\ \\ \text{Multiplying this out:}&12C+12C-120=C^2-10C \\ \\ \text{Which simplifies to}&C^2-34C+120=0 \\ \\ \text{Which will factor to}& (C-30)(C-4) = 0 \end{array}[/latex]

Cosmo can build the large shed in either 30 days or 4 days. Joey, therefore, can build the shed in 20 days or −6 days (rejected).

The solution is Cosmo takes 30 days to build and Joey takes 20 days.

Example 9.10.4

Clark can complete a job in one hour less than his apprentice. Together, they do the job in 1 hour and 12 minutes. How long would it take each of them working alone?

[latex]\begin{array}{rl} \text{Convert everything to hours:} & 1\text{ h }12\text{ min}=\dfrac{72}{60} \text{ h}=\dfrac{6}{5}\text{ h}\\ \\ \text{The equation to solve is} & \dfrac{1}{A}+\dfrac{1}{A-1}=\dfrac{1}{\dfrac{6}{5}}=\dfrac{5}{6}\\ \\ \text{Therefore the equation is} & \dfrac{1}{A}+\dfrac{1}{A-1}=\dfrac{5}{6} \\ \\ \begin{array}{r} \text{To remove the fractions, } \\ \text{multiply each term by the LCD} \end{array} & (A)(A-1)(6)\\ \\ \text{This leaves} & 6(A)+6(A-1)=5(A)(A-1) \\ \\ \text{Multiplying this out gives} & 6A-6+6A=5A^2-5A \\ \\ \text{Which simplifies to} & 5A^2-17A +6=0 \\ \\ \text{This will factor to} & (5A-2)(A-3)=0 \end{array}[/latex]

The apprentice can do the job in either [latex]\dfrac{2}{5}[/latex] h (reject) or 3 h. Clark takes 2 h.

Example 9.10.5

A sink can be filled by a pipe in 5 minutes, but it takes 7 minutes to drain a full sink. If both the pipe and the drain are open, how long will it take to fill the sink?

The 7 minutes to drain will be subtracted.

[latex]\begin{array}{rl} \text{The equation to solve is} & \dfrac{1}{5}-\dfrac{1}{7}=\dfrac{1}{X} \\ \\ \begin{array}{r} \text{To remove the fractions,} \\ \text{multiply each term by the LCD}\end{array} & (5)(7)(X)\\ \\ \text{This leaves } & (7)(X)-(5)(X)=(5)(7)\\ \\ \text{Multiplying this out gives} & 7X-5X=35\\ \\ \text{Which simplifies to} & 2X=35\text{ or }X=\dfrac{35}{2}\text{ or }17.5 \end{array}[/latex]

17.5 min or 17 min 30 sec is the solution

For Questions 1 to 8, write the formula defining the relation. Do Not Solve!!

Bill’s father can paint a room in 2 hours less than it would take Bill to paint it. Working together, they can complete the job in 2 hours and 24 minutes. How much time would each require working alone?
Of two inlet pipes, the smaller pipe takes four hours longer than the larger pipe to fill a pool. When both pipes are open, the pool is filled in three hours and forty-five minutes. If only the larger pipe is open, how many hours are required to fill the pool?
Jack can wash and wax the family car in one hour less than it would take Bob. The two working together can complete the job in 1.2 hours. How much time would each require if they worked alone?
If Yousef can do a piece of work alone in 6 days, and Bridgit can do it alone in 4 days, how long will it take the two to complete the job working together?
Working alone, it takes John 8 hours longer than Carlos to do a job. Working together, they can do the job in 3 hours. How long would it take each to do the job working alone?
Working alone, Maryam can do a piece of work in 3 days that Noor can do in 4 days and Elana can do in 5 days. How long will it take them to do it working together?
Raj can do a piece of work in 4 days and Rubi can do it in half the time. How long would it take them to do the work together?
A cistern can be filled by one pipe in 20 minutes and by another in 30 minutes. How long would it take both pipes together to fill the tank?

For Questions 9 to 20, find and solve the equation describing the relationship.

If an apprentice can do a piece of work in 24 days, and apprentice and instructor together can do it in 6 days, how long would it take the instructor to do the work alone?
A carpenter and his assistant can do a piece of work in 3.75 days. If the carpenter himself could do the work alone in 5 days, how long would the assistant take to do the work alone?
If Sam can do a certain job in 3 days, while it would take Fred 6 days to do the same job, how long would it take them, working together, to complete the job?
Tim can finish a certain job in 10 hours. It takes his wife JoAnn only 8 hours to do the same job. If they work together, how long will it take them to complete the job?
Two people working together can complete a job in 6 hours. If one of them works twice as fast as the other, how long would it take the slower person, working alone, to do the job?
If two people working together can do a job in 3 hours, how long would it take the faster person to do the same job if one of them is 3 times as fast as the other?
A water tank can be filled by an inlet pipe in 8 hours. It takes twice that long for the outlet pipe to empty the tank. How long would it take to fill the tank if both pipes were open?
A sink can be filled from the faucet in 5 minutes. It takes only 3 minutes to empty the sink when the drain is open. If the sink is full and both the faucet and the drain are open, how long will it take to empty the sink?
It takes 10 hours to fill a pool with the inlet pipe. It can be emptied in 15 hours with the outlet pipe. If the pool is half full to begin with, how long will it take to fill it from there if both pipes are open?
A sink is ¼ full when both the faucet and the drain are opened. The faucet alone can fill the sink in 6 minutes, while it takes 8 minutes to empty it with the drain. How long will it take to fill the remaining ¾ of the sink?
A sink has two faucets: one for hot water and one for cold water. The sink can be filled by a cold-water faucet in 3.5 minutes. If both faucets are open, the sink is filled in 2.1 minutes. How long does it take to fill the sink with just the hot-water faucet open?
A water tank is being filled by two inlet pipes. Pipe A can fill the tank in 4.5 hours, while both pipes together can fill the tank in 2 hours. How long does it take to fill the tank using only pipe B?

Answer Key 9.10

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how to solve work and time problems

Learning Point - Guidely

How to solve work and time problems.

Time and work are related with the time taken by a person or a group of persons to complete a task and the efficiency of the work done by each of them. Here we have provided detailed information about how to solve work and time problems.

Step 1: To find one day work

If A can do a piece of work in 10 days, then A’s one day work will be 1/10.

Step 2: Work and Wages

Ratio of wages of persons doing work is directly proportional to the ratio of efficiency of the persons.

Step 3: To find the Ratio

If 'A' is 'x' times as good a workman as 'B', then

Ratio of work done by A & B in equal time = x: 1
Ratio of time taken by A & B to complete the work = 1: x. This means that 'A' takes (1/xth) time as that of 'B' to finish the same amount of work.

Step 4: To Find Efficiency

Efficiency is directly proportional to the work done and inversely proportional to the time taken.

Step 5: number of days required to complete the work by A and B

The number of days or time required to complete the work by A and B both is equal to the ab/a+b.

Step 6: Know the Important Time and Work Formulas

Before going to approach time and work problems you have to be proficient with the important time and work formulas. We have given the time and work formula pdf download link below. Candidates can utilize this formula pdf to solve time and work problems easily.

Click Here To Download Time and Work Formula PDF

Step 7: Practice Time and Work Questions

Practice time and work questions regularly will help you to improve your speed and accuracy while solving the time and work questions on the real exams. So practice is the only key to acing this time and work topic.

Click Here To Practice Time and Work Questions

Click Here To Download More Quantitative Aptitude Formulas PDFs and Tricks

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Time and Work Concepts, Tricks and Formulas | Time and Work Questions

Time and Work is the widely asked topic in every exam for the past many years. If you are preparing for any government exam, then your concept of this topic should be very clear. Let’s revise all the concepts of Time and work from this article and learn time and work tricks to save time in exams through the following time and work-study notes.

Concept of Time and Work

Time: Time is the duration during which any activity or work happens or continues.

Work: Work is a task or set of activities to achieve a certain result.

We can define happening of work as:

If a person A completes a work in X days, then the amount of work completed by him in 1 day will be = ${1 \over X}$
Similarly, if a person B completes work in Y days, then the amount of work completed by him in 1 day will be = ${1 \over Y}$
From the above two points, we can say that in one day A and B together can complete ${({1 \over X}+{1 \over Y})}$ amount of work. Thus, together A and B can complete the work in $\frac{XY} {X+Y}$ days.

Here, we have assumed total work as 1 unit. Similarly, we can assume our total work as anything as per our convenience. The best assumption for easing out our calculations of the total work is assuming work as 100% or LCM of time taken by all the persons.

Points to Remember:

Every work requires a particular amount of time.
Work done is directly proportional to the time taken. And, the proportionality sign is removed by efficiency/one-day work/work rate.

Work done = Efficiency × Time taken

Let us understand the concept through a question

Example: - The time taken by Ram and Shyam alone to complete a piece of work is 24 days and 40 days, respectively. What is the time taken by Ram and Shyam together to complete the same amount of work?

Solution: -

Ram complete the whole work in 24 days

So, part of the work done by Ram in one day = $\frac{1}{24}$

Shyam complete the whole work in 40 days

So, part of the work done by Shyam in one day = $\frac{1}{40}$

Therefore, one day work of Ram and Shyam together will be

$⇒\frac{1}{24}+\frac{1}{40}=\frac{8}{120}$

As Ram and Shyam together can complete 8/120 part of the work in 1 day

So, time taken by Ram and Shyam together to complete the work will be = $\frac{120}{8}=15$ days

Alternative Method:

Step 1: Assuming a total work

Let us assume the total work be LCM of (24 and 40) = 120 units

Step 2: Calculating the efficiency of each individual

Work done = time taken × Efficiency(or one-day work)

⇒ Efficiency of Ram = 120/24 = 5 units/day

⇒ Efficiency of Shyam = 120/40 = 3 units/day

You can depict the above-calculated information in the format shown below:

Step 3: Calculating the combined efficiency

From the above figure,

Efficiency of Ram and Shyam together will be = 5 + 3 = 8 units/day

${Time \space taken \space by \space \space Ram \space and \space Shyam\space \space to \space complete\space the work=\dfrac{Total \space work}{Efficiency}}$

$⇒\dfrac{120}{8}=15 \space days$

You can also attempt the Quiz based on Time and Work:

1. Time and Work Practice Quiz 1

2. Time and Work Practice Quiz 2

Different types of Time and Work questions in an exam

Let’s see how questions in various exams from time and work are generally asked:

Example: Three men A, B, and C can complete a piece of work in 15, 24 and 40 days, respectively.

If A and B together have started the work and did work for 4 days, then the remaining work will be completed by C in how many days?
If A, B and C together have started the work, but 2 days after the start of work, A left the work while B left the work three days before the completion of the work, then in how many days total work gets completed?

Let us assume the total work be LCM of (15, 24 and 40) = 120 units

Work done = time taken × Efficiency (or one-day work)

Here, it is given that A and B started the work together

So, efficiency of A and B together will be = 8 + 5 = 13 units/day

Now, the amount of work done by A and B together in 4 days will be = 13 * 4 = 52 units

Thus, remaining work = 120 – 52 = 68 units

As remaining work is to be done by only C

So, time taken by C to complete the remaining work will be

$=\dfrac{Work}{Efficiency}=\dfrac{68}{3}=22\dfrac{2}{3} \space days$

Here, it is given that A, B and C together have started the work

So, efficiency of A, B and C together will be = 8 + 5 + 3 = 16 units/day

Amount of work done by A, B and C together in 2 days = 16 * 2 = 32 units

Now, remaining work = 120 – 32 = 88 units

As B left the work three days before the completion of the work

So, amount of work done by C in 3 days = 5 * 3 = 15 units

Thus, remaining work = 88 – 15 = 73 units

Here, we can say that the remaining work will be done by B and C together

Efficiency of B and C together will be = 5 + 3 = 8 units/day

Time taken by B and C together to complete the remaining 73 units of work

$=\dfrac{73}{8}=9\dfrac{1}{8} \space days$

⇒ Total time taken to complete the work $= 2+9\dfrac{1}{8}+3=14\dfrac{1}{8} \space days$

Note: If A working alone takes ‘d 1 ’ days more than A and B together, and B working along takes ‘d 2 ’ days more than A and B together, then the number of days taken by A and B working together will be $\sqrt {d_1d_2}$

Example: - Brij alone takes 3 days more than Brij and Mohan together to complete work while Mohan takes 12 days more than Brij and Mohan together, then in how many days Brij and Mohan together can complete the work?

Solution: - Here, d 1 = 3 and d 2 = 12

So, Time taken by Brij and Mohan to complete the work together will be = $\sqrt{3*12}=\sqrt{36}=6 \space days$

Concept of Efficiency

Efficiency denotes the amount of work done by any person in 1 day. We use this concept to compare the quality of a worker, i.e., if a worker is more efficient than any other worker, then we can say he/she can do more work in 1 day as compared to other workers.

The ratio of the efficiencies of two workers is inversely proportional to the time taken by them to complete a work.

If a worker is less efficient than he/she will take more time to complete the work.
If a worker is more efficient than he/she will take less time to complete the work.
The number of workers is inversely proportional to the time taken to complete the work.

Example: - A is 3 times as efficient as B. If B alone can complete the work in 12 days, then A alone can complete the work in how many days?

Solution: - According to the question, the ratio of the efficiency of A and B is 3 : 1

We know that the ratio of the efficiency is inversely proportional to the ratio of the time taken

So, the ratio of the time taken by A and B to complete the work will be 1 : 3

Let us assume A alone completes the work in x days and B alone completes the work in 3x days

Therefore, A alone can complete the work in 4 days.

Note: The concept of efficiency is widely used to equate the works of men, women, and children.

Let us understand the application of the concept of efficiency through a question

Example: - 8 men and 7 women can complete a piece of work in 15 days while 6 men and 3 women can complete a piece of work in 30 days. In how many days 1 woman can complete the total work?

Solution: - Let us assume efficiencies or one day work of 1 man and 1 woman are M and W respectively

So, the efficiency of 8 men = 8M and efficiency of 7 women = 7W

Similarly, efficiency of 6 men = 6M and efficiency of 3 women = 3W

Work done = time taken × Efficiency

According to question, 8 men and 7 women can complete a piece of work in 15 days

So, Total work done = (Efficiency of 8 men and 7 women) × Time taken

⇒ Total work done = (8M + 7W) * 15 = 120M + 105W …… (1)

Similarly, 6 men and 3 women can complete a piece of work in 30 days

So, Total work done = (Efficiency of 6 men and 3 women) × Time taken

⇒ Total work done = (6M + 3W) * 30 = 180M + 90W ….. (2)

As, total work done is same so

120M + 105W = 180M + 90W

From the above equation we can say that efficiency of 1 woman is equal to the efficiency of 4 men

Now, from equation (1)

Total work done = 120M + 105W

$⇒Total \space work \space done=\dfrac{120}{4}W+105W=135W$

Therefore, time taken by 1 woman to complete the work will be

$⇒\dfrac{135W}{1W}=135 \space days$

Work and Wages

The Concept of work and wages is used to compare the work with the remuneration for the work. The wages for any amount of work is directly proportional to the work done.

If all the workers work for the same number of days, then their wages are in the ratio of their efficiencies.
If all the workers have the same efficiencies and do the work for the different number of days, then their wages are distributed in the ratio of the number of days for which each of them worked.
If the workers have different efficiency and do the work for the different number of days, then their wages are in the ratio of the work done by them.

MDH formula

MDH formula is used to compare the works of the same nature done at two different times using different manpower. The MDH formula can be represented as

$\dfrac{M_1D_1H_1E_1}{W_1}=\dfrac{M_2D_2H_2E_2}{W_2}$

Where M denotes the number of men/women, D denotes the number of days, H denotes the number of hours in a day, E denotes the efficiency of 1 man, and W denotes part of work done

Let us understand the application of this formula using a question

Example: - 20 men working 10 hours per day can finish 2/3 rd of the work in 12 days, while 15 women working 9 hours per day can finish 2/5 th of the work in X days. If one woman is twice as efficient as one man, then what is the value of X?

M 1 = 20, D 1 = 12, H 1 = 10, W 1 = $2 \over 3$ , M 2 = 15, D 2 = X, H 2 = 9, W 2 = $2 \over 5$

According to the question, one woman is twice as efficient as one man

So, the ratio of efficiency of woman and man is 2 : 1

$⇒\dfrac{E_2}{E_1}=\dfrac{2}{1}$

Now, using MDH formula we get

${⇒\dfrac{20*12*10}{\dfrac{2}{3}}=\dfrac{15*X*9}{\dfrac{2}{5}}*\dfrac{E_2}{E_1}}$

$⇒\dfrac{2400*3}{2}=\dfrac{135*5*X}{2}*2$

$⇒X=5\dfrac{1}{3} \space days$

Pipe and Cistern

In the case of pipe and cistern problems, all the above concepts of time and work are applied. One more concept of negative work also comes into play on this topic. To check how questions on Pipe and cistern are asked in various exams and read in detail about Pipe and cistern .

Read the Divisibility Rules of Natural Numbers from 1 to 19.

Frequently Asked Questions (FAQs)

Q 1. what is the best method to master time and work topic, q 2. i am not from technical background can i score well in this topic, q 3. what is the weightage of time and work in different exams like ssc, cat, banking, and railways, q 4. i could not score well in "time and work" topic what should i do, q 5. how time is related to work, q 6. which is the best book to practice questions of time and work, celebrate mother's day get 35% off use coupon code mom35off.

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Problems on Time and Work

Learn how to solve problems on time and work in different situations when time required to complete a piece of work and when the work done in a given period of time.

Case I: If a person A completes a piece of work in n days, then work done by A in one days = 1/n th part of the work.

Case II: If a person A completes 1/n th part of work in one day, then A will take n days to complete the work.

Now we will learn how to use the concept of time and work for solving various problems.

Word problems on time and work:

1. Adam is thrice as good a workman as Brain and together they finish the piece of work in 15 days. In how many days will Adam alone finish the work?

Adam’s 1 day’s work: Brain’s 1 day’s work = 3 : 1

(Adam + Brain)’s 1 day’s work = 1/15

Now, divided 1/15 in the ratio 3 : 1

Therefore, Adam’s 1 day’s work = 1/15 × 3/4 = 1/20

Therefore, Adam alone can finish the work in 20 days.

2. Archie, Benjamin, Christopher can finish a piece of work in 10 days, 12 days and 15 days respectively. If all the three work at it together, they are paid $ 600 for the whole work. How should the money be divided among them?

Solution:

Archie’s 1 day’s work = 1/10

Benjamin’s 1 day’s work = 1/12

Christopher’s 1 day’s work = 1/15

Therefore, ratio of shares of Archie, Benjamin, Christopher = Ratio of their 1 day’s work.

= 1/10 : 1/12 : 1/15

= 6 : 5 : 4

Sum of ratio terms = 6 + 5 + 4 = 15

Therefore, Archie’s share = $ 6/15 × 600 = 6 × 40 = $ 240

Benjamin’s share = $ 5/15 × 600 = 5 × 40 = $ 200

Christopher’s share = $ 4/15 × 600 = 4 × 40 = $ 160

Calculate Time to Complete a Work

Calculate Work Done in a Given Time

Problems on Time required to Complete a Piece a Work

Problems on Work Done in a Given Period of Time

Pipes and Water Tank

Problems on Pipes and Water Tank

7th Grade Math Problems From Problems on Time and Work to HOME PAGE

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"Work" Word Problems

Painting & Pipes Tubs & Man-Hours Unequal Times Etc.

"Work" problems usually involve situations such as two people working together to paint a house. You are usually told how long each person takes to paint a similarly-sized house, and you are asked how long it will take the two of them to paint the house when they work together.

Many of these problems are not terribly realistic — since when can two laser printers work together on printing one report? — but it's the technique that they want you to learn, not the applicability to "real life".

The method of solution for "work" problems is not obvious, so don't feel bad if you're totally lost at the moment. There is a "trick" to doing work problems: you have to think of the problem in terms of how much each person / machine / whatever does in a given unit of time . For instance:

Content Continues Below

MathHelp.com

Suppose one painter can paint the entire house in twelve hours, and the second painter takes eight hours to paint a similarly-sized house. How long would it take the two painters together to paint the house?

To find out how much they can do together per hour , I make the necessary assumption that their labors are additive (in other words, that they never get in each other's way in any manner), and I add together what they can do individually per hour . So, per hour, their labors are:

But the exercise didn't ask me how much they can do per hour; it asked me how long they'll take to finish one whole job, working togets. So now I'll pick the variable " t " to stand for how long they take (that is, the time they take) to do the job together. Then they can do:

This gives me an expression for their combined hourly rate. I already had a numerical expression for their combined hourly rate. So, setting these two expressions equal, I get:

I can solve by flipping the equation; I get:

An hour has sixty minutes, so 0.8 of an hour has forty-eight minutes. Then:

They can complete the job together in 4 hours and 48 minutes.

The important thing to understand about the above example is that the key was in converting how long each person took to complete the task into a rate.

hours to complete job:

first painter: 12

second painter: 8

together: t

Since the unit for completion was "hours", I converted each time to an hourly rate; that is, I restated everything in terms of how much of the entire task could be completed per hour. To do this, I simply inverted each value for "hours to complete job":

completed per hour:

Then, assuming that their per-hour rates were additive, I added the portion that each could do per hour, summed them, and set this equal to the "together" rate:

adding their labor:

As you can see in the above example, "work" problems commonly create rational equations . But the equations themselves are usually pretty simple to solve.

One pipe can fill a pool 1.25 times as fast as a second pipe. When both pipes are opened, they fill the pool in five hours. How long would it take to fill the pool if only the slower pipe is used?

My first step is to list the times taken by each pipe to fill the pool, and how long the two pipes take together. In this case, I know the "together" time, but not the individual times. One of the pipes' times is expressed in terms of the other pipe's time, so I'll pick a variable to stand for one of these times.

Since the faster pipe's time to completion is defined in terms of the second pipe's time, I'll pick a variable for the slower pipe's time, and then use this to create an expression for the faster pipe's time:

slow pipe: s

together: 5

Next, I'll convert all of the completion times to per-hour rates:

Then I make the necessary assumption that the pipes' contributions are additive (which is reasonable, in this case), add the two pipes' contributions, and set this equal to the combined per-hour rate:

multiplying through by 20 s (being the lowest common denominator of all the fractional terms):

20 + 25 = 4 s

45/4 = 11.25 = s

They asked me for the time of the slower pipe, so I don't need to find the time for the faster pipe. My answer is:

The slower pipe takes 11.25 hours.

Note: I could have picked a variable for the faster pipe, and then defined the time for the slower pipe in terms of this variable. If you're not sure how you'd do this, then think about it in terms of nicer numbers: If someone goes twice as fast as you, then you take twice as long as he does; if he goes three times as fast as you, then you take three times as long as him. In this case, if he goes 1.25 times as fast, then you take 1.25 times as long. So the variables could have been " f " for the number of hours the faster pipe takes, and then the number of hours for the slower pipe would have been " 1.25 f ".

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How to Solve Combined Labor Problems

Last Updated: November 3, 2023 Fact Checked

This article was reviewed by Grace Imson, MA . Grace Imson is a math teacher with over 40 years of teaching experience. Grace is currently a math instructor at the City College of San Francisco and was previously in the Math Department at Saint Louis University. She has taught math at the elementary, middle, high school, and college levels. She has an MA in Education, specializing in Administration and Supervision from Saint Louis University. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. This article has been viewed 82,120 times.

Combined labor problems, or work problems, are math problems involving rational equations. [1] X Research source These are equations that involve at least one fraction. The problems basically require finding unit rates, combining them, and setting them equal to an unknown rate. These problems require a lot of interpretive logic, but as long as you know how to work with fractions, solving them is fairly easy.

Problems with Two People Working Together

For example, the problem might ask, “If Tommy can paint a room in 3 hours, and Winnie can paint the same room in 4 hours, how long will it take them to paint the room together?

Step 2 Determine the hourly rate of each individual.

Problems with Two People Working Against Each Other

For example, the problem might ask, “If a hose can fill a pool 6 hours, and an open drain can empty it in 2 hours, how long will it take the open drain to empty the pool with the hose on?”

Step 2 Determine the hourly rate of the individual completing the job.

Problems with Two People Working In Shifts

For example, the problem might be: “Damarion can clean the cat shelter in 8 hours, and Cassandra can clean the shelter in 4 hours. They work together for 2 hours, but then Cassandra leaves to take some cats to the vet. How long will it take for Damarion to finish cleaning the shelter on his own?”

Community Q&A

If the problem involves more than two workers, simply add their individual work rates, then take the reciprocal of the sum to get the time taken working together. Thanks Helpful 2 Not Helpful 0
Pay close attention to units. These methods will work for any unit of time, such as minutes or days. Some problems might state the rates in different units, and you will need to convert. Thanks Helpful 0 Not Helpful 0

Things You'll Need

A calculator

↑ http://www.mathguide.com/lessons/Word-Work.html
↑ http://www.algebralab.org/Word/Word.aspx?file=Algebra_WorkingTogether.xml
↑ https://www.mtsac.edu/marcs/worksheet/math51/course/10application_problems_rational_expressions.pdf
↑ http://purplemath.com/modules/workprob2.htm

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Time & Work - Solved Examples

Q 1 - A can do a bit of work in 8 days, which B alone can do in 10 days in how long . In how long both cooperating can do it?

A - 40/9 days

B - 41/9 days

C - 42/9 days

D - 43/9 days

Explanation

Q 2 - A and B together can dive a trench in 12 days, which an alone can dive in 30 days. In how long B alone can burrow it?

A - 18 days

B - 19 days

C - 20 days

D - 21 days

Q 3 - A can do a bit of work in 25 days which B can complete in 20 days. Both together labor for 5 days and afterward A leaves off. How long will B take to complete the remaining work?

D - 11 days

Q 4 - A and B can do a bit of work in 12 days. B and C can do it in 15 days while C and A can do it in 20 days. In how long will they complete it cooperating? Additionally, in how long can A alone do it?

A - 10 days, 30 days.

B - 15 days, 20 days.

C - 20 days, 40 days.

D - 10 days, 50 days.

Q 5 - A can fabricate a divider in 30 days , while B alone can assemble it in 40 days, If they construct it together and get an installment of RS. 7000, what B's offer?

Q 6 - A can do a bit of work in 10 days while B alone can do it in 15 days. They cooperate for 5 days and whatever remains of the work is finished by C in 2 days. On the off chance that they get Rs. 4500 for the entire work, by what means if they partition the cash?

A - Rs 1250, Rs 1200, Rs 550

B - Rs 2250, Rs 1500, Rs 750

C - Rs 1050, Rs 1000, Rs 500

D - Rs 650, Rs 700, Rs 500

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Work From Days

Work from Days section will ask you questions in which you will have to calculate the amount of work that we can perform in some time. In a similar manner to the concept of days from work, the work from days section is easily solved by the application of some basic concepts and the formulae that we will develop. Here we have solved examples and all the important concepts that you may have to answer while solving this section. Let us see.

Solved Example

Example 1: Ten people can cut 20 trees in 2 days. If twenty people work for two months, then how many trees will be cut during this time?

A) 1330 trees B) 1223 trees C) 1220 trees D) 1222 trees

Answer: We will use the formula w 1 /w 2 = (T 1 × N 1 )/(T 2 × N 2 ) that we have developed just above. Here w 1 = 20, T 1 = 2 and N 1 = 10.

Similarly, we have w 2 = ? , T 2 = 61 days, and N 2 = 20. Substituting these values in the equation above, we have:

w 1 /w 2 = (T 1 × N 1 )/(T 2 × N 2 ). In other words we can say: 20/w 2 = (2×10)/(61×20).

Solving this we can say that w 2 = 1220 trees.

We can use the same formula to solve similar questions. Let us now see an important concept that will simplify a lot of our problems. The concept of efficiency in work. Hence the correct option is C) 1220 trees.

Efficiency Of Work

The efficiency is the amount of work that a person can do in some certain time. For example, consider the following example:

Example 2: What is the efficiency of a person who finishes his job in 5 days?

Answer: As per the question, the number of days this person takes to complete the work = 5 Therefore we can say that he does 1/5th of the work per day. This when we convert it into percentage = 100/5 = 20%. Therefore, his efficiency is 20%.

We can use the efficiency to solve many problems in a very short time. Let us see how.

Example 3: A person ‘A’ can do a job in 10 days. Another person ‘B’ can do the same job in 5 days. In how many days will they complete this job if they work together?

Answer: As per the question, we have A’s efficiency = 10% and B’s efficiency = 20%. Therefore when they work together, their efficiency is = A+ B = 10 + 20 = 30% This means, in one day A and B together can do 30% of work. Therefore, the number of days it will take A and B together to do 100% of the work = 100/30 = 3.33 days.

Some Solved Examples

Example 4: A and B can do a job in 8 days. B and C can do the same job in 12 days. When A, B, and C work together, they can do the same job in 6 days. In how many days can A and C complete this job?

Answer: As per the question we have: The combined efficiency of A and B is = (A+B’s) efficiency = 12.5% Also, we have: B+C’s efficiency = 8.33% And A+B+C’s efficiency = 16.66% Now we need to find A + C. Let us see how to solve this:

Consider, the expression 2(A+B+C), we can write it as = (A+B) + (B+C) + (C+A) Therefore we have 2(16.66) = 12.5+ 8.33 + (C+A) And hence we have: C+A = 12.49 = 12.5% Therefore, the time that A and C take = 100/12.5 = 8 days.

Example 5: A person A is twice as efficient as another person B. The person A can complete a job 30 days before B. If they work together, how long will it take them to finish the job?

Answer: Let the efficiency of B = x and thus the efficiency of A = 2x. Since the person A takes 30 days to complete a job, the person B will take 60 days to complete the same job.

A’s efficiency = 1/30 = 3.33% B’s efficiency = 1/60 = 1.66% Therefore there combined efficiency for this job = 3.33% + 1.66% = 5% of the job in 1 day. So they can complete the whole job in 20 days (= 100/5 days).

Practice Questions

Q 1: A and B together can complete a task in 20 days. B and C together can complete the same task in 30 days. A and C together can complete the same task in 30 days. What is the respective ratio of the number of days taken by A when completing the same task alone to the number of days taken by C when completing the same task alone?

A) 3:1 B) 3:2 C) 1:3 D) 2:3

Ans: C) 1:3

Q 2: A does 80% of a work in 20 days. He then calls in B and they together finish the remaining work in 3 days. How long B alone would take to do the whole work?

A) 37 (1/2) B) 36 C) 39 (1/2) D) 40

Ans: 37 (1/2)

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Work And Time

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2 responses to “Work From Days”

ans for last ques. is 38.5

no..answer is correct

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Formulas For Time and Work

November 4, 2023

Time and Work Formulas

Go through the entire page to know easy Formulas For Time and Work that will help you to solve problems quickly.

Formula's For Time and Work

Work from days:.

If A can do a piece of work in n days, then A’s one day work = \frac{1}{n}

Days from work:

If A’s one day work = \frac{1}{n} , then A can finish the work in n days

Work Done by A and B

A and B can do a piece of work in ‘a’ days and ‘b’ days respectively.

When working together they will take \frac{ab}{a+b} days to finish the work

In one day, they will finish \frac{a+b}{ab} part of work.

If A is thrice as good a workman as B, then:

Ratio of work done by A and B = 3: 1.

Ratio of times taken by A and B to finish a work = 1: 3

Efficiency:

Efficiency is inversely proportional to the

Time taken when the amount of work done is constant.

Efficiency α = \frac{1}{Time Taken}

Rules for Time and Work

Rule 1: If A completes a piece of work in x days. And B can completes same piece of work in y days .

One day work of A = \frac{1}{x} One day work of B = \frac{1}{y}

Work done by A + B = \frac{1}{x} + \frac{1}{y} = \frac{x+y}{xy}

Total time = \frac{xy}{x + y}

Rule 2: If A completes a piece of work in x days. B completes same piece of work in y days .C completes same piece of work in z days

One day work of A = \frac{1}{x}

One day work of B = \frac{1}{y}

One day work of C = \frac{1}{z}

Work done by A + B + C = \frac{1}{x} + \frac{1}{y} + \frac{1}{z} = \frac{yz+xz+xy}{xyz}

Total time = \frac{xyz}{xy + yz + zx} .

Rule 3 : If M 1 men can complete a work W 1 in D 1 days and M 2 men can complete a work W 2 in D 2 days then , \frac{M_{1}D_{1}}{W_{1}} = \frac{M_{2}D_{2}}{W_{2}} .

If Time required by Both M 1 and M 2 is T 1 and T 2 respectively, then relation is \frac{M_{1}D_{1}T_{1}}{W_{1}} = \frac{M_{2}D_{2}T_{2}}{W_{2}}

Rule 4: If A alone can complete a certain work in ‘x’ days and A and B together can do the same amount of work in ‘y’ days,

Work done by b = \frac{1}{y} – \frac{1}{x} = \frac{x-y}{xy}

Then B alone can do the same work in \frac{xy}{(x-y)} days

Rule 5: If A and B can do work in ‘x’ days.

If B and C can do work in ‘y’ days.

If C and A can do work in ‘z’ days.

Work done by A,B and C = \left ( \frac{1}{2}\right )\left ( \frac{1}{x}+\frac{1}{y}+\frac{1}{z} \right )

Total time taken when A, B, and C work together \frac{2xyz}{ ( xy+yz+zx )}

Rule 6: Work of one day = \frac{Total work}{Total number of working days}

Total work = one day work × Total number of working days

Remaining work = 1 – work done

Work done by A = A’s one day work × Total number of working days of A

Rule 7: If A can finish \frac{m}{n} part of the work in D days.

Then total time taken to finish the work by A = \frac{D}{\frac{m}{n}} = \frac{n}{m} × D days

If A can do a work in ‘x’ days

B can do the same work in ‘y’ days

When they started working together, B left the work ‘m’ days before completion then total time taken to complete the work = (y+m)x/(x+y)

Rule 9: A and B finish work in a days.

They work together for ‘b days and then A or B left the work.

B or A finished the rest of the work in ‘d’ days.

Total time taken by A or B alone to complete the work = \frac{ad}{a – b} or \frac{bd}{a-b}

Questions based on above formulas:

Question 1: A construction crew of 8 workers can build a house in 24 days. How many days will it take for 12 workers to build the same house?

Answer: Let the amount of work required to build the house be represented as “1 house.” 8 workers can build the house in = 24 days Day taken by 12 workers to build the house = \frac{8 \times 24}{12}

= {8 \times 2}

Question 2: A bakery can bake 180 cakes in 6 days. How many cakes can it bake in 10 days?

Answer: Let the amount of work required to paint the house be represented as “1 house.” Time taken by 15 painters to paint a house = 9 days

Time taken by 9 painters to paint the same house =

\frac{15 \times 9}{9}

= {15 \times 1}

Question 4: A machine can produce 240 widgets in 5 days. How long will it take for the machine to produce 600 widgets?

Question 5 : If a team of 6 workers can complete a project in 18 days, how many workers are needed to complete the project in 9 days?

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Speed Time and Distance – Questions | Formulas | How to Solve Quickly | Tricks & Shortcuts
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Pipes and Cisterns – Questions | Formulas | How to Solve Quickly | Tricks & Shortcuts
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Pipes and Cisterns – Questions | Formulas | How to Solve Quickly | Tricks & Shortcuts

Work Problems: Basic Concepts

If you like to learn by example, jump right to Work Problems: Guided Practice . For a more thorough approach, keep reading—this section covers all the concepts needed to successfully solve work problems. After mastering this section, you'll be ready for Work Problems: Quick-and-Easy Estimates .

A Typical Work Problem

Carol mows a lawn in 5 hours. Julia mows the same lawn in only 3 hours. How long will it take if they mow the lawn together?

Table of Contents for This Web Page

Choose Your Own Names! (Personalize all the practice problems on this page)
Different Types of Work Problems (Guessing Game)
Rates in Work Problems (Quick Check)
Individual Rates versus Combined Rates (Quick Check)
When Does the Sum of the Individual Rates Give the Combined Rate? (Quick Check)
Rates Have Lots of Different Names (Sentence Shuffle)

The practice problems in this section will be MORE FUN if they use people you know!

So... take a minute and put in some names!

Think of a name. Type it in the name box below.
Is the name you're thinking of male or female ? Click the appropriate male/female button.
Click the ‘Add this name!’ button.
Put in as many or as few as you want. (We may throw in some of our own, just to spice things up.)
Refresh this page if you want to throw everything away and start over.

Different Types of Work Problems

In a work problem, we know some information about how quickly a job can be done. For example, we might know how fast each person could do it, if they work alone. However, there's always something that we don't know, and want to figure out.

In a work problem, it might not even be people doing the work! The job might be done by animals, or machines, or—use your imagination! However, in this discussion, we'll have people do the job, just to keep things simple.

The following ‘Guessing Game’ introduces you to several types of work problems, and develops your intuition for reasonable solutions.

Rates in Work Problems

Work problems always involve rates . Recall from Rate Problems that:

For example, these are all rates:

5 dollars per hour, also written as $\displaystyle\ \frac{\$5}{\rm hr}$
1 job per 3 seconds, also written as: $$\text{1 job/3 sec}\ \ \text{ or } \ \ \frac{1{\rm\ job}}{3{\rm\ sec}}\ \ \text{ or }\ \ \frac 13\ \frac{\rm\ job}{\rm\ sec}$$
10 kilograms per cubic inch, also written as: $$\text{10 kg/}\text{in}^3\ \ \text{ or }\ \ \frac{10{\rm\ kg}}{ { \rm in}^3}$$

Work problems typically involve rates with a unit of time in the denominator.

That is, you might see

in a work problem, because these denominators are both units of time.

However, you won't typically see $\ \frac{10\text{ kg}}{\text{in}^3}\ $ in a work problem, because it doesn't have a unit of time in the denominator.

Individual Rates versus Combined Rates

In a two-person work problem, there are always three rates involved:

the rate the job is done when the first person works alone
the rate the job is done when the second person works alone
the rate the job is done when both people work together

The first two rates are called the individual rates , and the last one is called the combined rate .

When Does the Sum of the Individual Rates Give the Combined Rate?

Under certain conditions, there is a simple relationship between the individual rates and the combined rate:

Consider, for example, the following scenario:

Suppose Carol types $\,5\,$ pages per hour, and Karl types $\,2\,$ pages per hour.

Will they be able to type $\,7\,$ pages together in one hour? (Note that $\,5 + 2 = 7\,.$ )

Maybe. Maybe not.

If there's only one typewriter between the two of them, then one will have to wait while the other types. They definitely won't be able to get $\,7\,$ pages done in one hour.

Or, suppose Carol and Karl can't ever get together without chatting, chatting, chatting. Then, they'll spend a lot of time talking, and not-so-much time typing. They definitely won't be able to get $\,7\,$ pages done in one hour. The combined rate will be less than $\,7\,$ pages/hour. The combined rate will be less than the sum of the individual rates.

So, under what circumstances will the sum of the individual rates equal the combined rate?

Answer: When the two people work together, the rates at which they work must remain exactly the same as if they were working alone.

If Carol can type $\,5\,$ pages per hour when she's all by herself, then she still types $\,5\,$ pages per hour when she's working with Karl.

If Karl can type $\,2\,$ pages per hour when he's all by himself, then he still types $\,2\,$ pages per hour when he's working with Carol.

In order to solve work problems, we have to assume that this relationship is true. Dr. Burns gives this assumption a special name—the Individual Rates Assumption:

Individual Rates Assumption

When two people work together, the rates at which they work remain exactly the same as if they were working alone.

( Under this assumption, the combined rate is the sum of the individual rates. )

Rates have Lots of Different Names

A rate is just an expression . Like all mathematical expressions, rates have LOTS of different names. The name you use for a rate depends on what you're doing with it.

Rates are easy to rename—just multiply by $\,1\,$ in an appropriate form! Here's an example, where we multiply by $\,1\,$ in the form of $\,\frac22\,$:

Want to know how many pages are typed in one hour? Then $\,\frac{5{\rm\ pages}}{\rm hr}\,$ is the best name.

Want to know how many pages are typed in two hours? Then $\,\frac{10{\rm\ pages}}{2\rm\ hr}\,$ is the best name.

Concept Practice

Algebra: Work Word Problems

Related Pages Math Work Problems Solving Work Word Problems Using Algebra More Algebra Lessons

In these lessons, we will learn

how to solve work problems that involve two persons.
how to solve work problems that involve more than two persons.
how to solve work problems that involve pipes filling up a tank.

What is a Work Word Problem?

Work word problems usually involve two or more entities working together to complete a task. Work problems have direct real-life applications. We often need to determine how many people are needed to complete a task within a given time. Alternatively, given a limited number of workers, we may need to determine how long it will take to finish a project. Here, we will deal with the basic math concepts of how to calculate work word problems.

How To Solve Work Word Problems For Two Persons?

This formula can be extended for more than two persons . It can also be used in problems that involve pipes filling up a tank .

Example 1: Peter can mow the lawn in 40 minutes and John can mow the lawn in 60 minutes. How long will it take for them to mow the lawn together?

Solution: Step 1: Assign variables : Let x = time to mow lawn together.

Step 3: Solve the equation The LCM of 40 and 60 is 120 Multiply both sides with 120

Answer: The time taken for both of them to mow the lawn together is 24 minutes.

Example 2: It takes Maria 10 hours to pick forty bushels of apples. Kayla can pick the same amount in 12 hours. How long will it take if they work together? Round your answer to the nearest hundredths.

“Work” Problems: More Than Two Persons

Example 1: Jane, Paul and Peter can finish painting the fence in 2 hours. If Jane does the job alone she can finish it in 5 hours. If Paul does the job alone he can finish it in 6 hours. How long will it take for Peter to finish the job alone?

Solution: Step 1: Assign variables : Let x = time taken by Peter

Example 2: Jim can dig a hole by himself in 12 hours. John can do it in 8 hours and Jack can do it in 6. How long will it take if they work together?

“Work” Problems: Pipes Filling Up A Tank

Example 1: A tank can be filled by pipe A in 3 hours and by pipe B in 5 hours. When the tank is full, it can be drained by pipe C in 4 hours. if the tank is initially empty and all three pipes are open, how many hours will it take to fill up the tank?

Solution: Step 1: Assign variables : Let x = time taken to fill up the tank

Step 3: Solve the equation

The LCM of 3, 4 and 5 is 60

Example 2: Pipe 1 takes 5 days to drain a pool and pipe 2 takes 7 days to drain the pool. How long will it take for the two pipes to drain the pool together?

Work Word Problems

It is possible to solve word problems when two people are doing a work job together by solving systems of equations. To solve a work word problem, multiply the hourly rate of the two people working together by the time spent working to get the total amount of time spent on the job. Knowledge of solving systems of equations is necessary to solve these types of problems.

Example: Latisha and Ricky work for a computer software company. Together they can write a particular computer program in 19 hours. Latisha can write the program by herself in 32 hours. How long will it take Ricky to write the program alone?

Example: A swimming pool is being drained through the drain at the bottom of the pool, and filled by the hose at the top. If the hose can fill the pool in 21 hours and the drain can empty the pool in 24 hours, how many hours will it take to fill the pool if the drain is left open? Express the answer in hours and round the answer to the nearest hour if needed.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.

Aptitude - Time and Work

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Time and Work - Formulas
Time and Work - General Questions
Time and Work - Data Sufficiency 1
Time and Work - Data Sufficiency 2
Time and Work - Data Sufficiency 3

Ratio of times taken by A and B = 1 : 3.

The time difference is (3 - 1) 2 days while B take 3 days and A takes 1 day.

If difference of time is 2 days, B takes 3 days.

So, A takes 30 days to do the work.

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Time and Work

Time and Work Questions

FACTS AND FORMULAE FOR TIME AND WORK QUESTIONS

1. If A can do a piece of work in n days, then A's 1 day's work = 1 n

2. If A’s 1 day's work = 1 n , then A can finish the work in n days.

3. A is thrice as good a workman as B, then:

Ratio of work done by A and B = 3 : 1.

Ratio of times taken by A and B to finish a work = 1 : 3.

NOTE :

E f f i c i e n c y ∝ 1 N o o f t i m e u n i t s

∴ E f f i c i e n c y × T i m e = C o n s tan t W o r k

Hence, R e q u i r e d t i m e = W o r k E f f i c i e n c y

Whole work is always considered as 1, in terms of fraction and 100% , in terms of percentage.

In general, number of day's or hours = 100 E f f i c i e n c y

A, B and C can do a piece of work in 24 days, 30 days and 40 days respectively. They began the work together but C left 4 days before the completion of the work. In how many days was the work completed?

One day's work of A, B and C = (1/24 + 1/30 + 1/40) = 1/10.

C leaves 4 days before completion of the work, which means only A and B work during the last 4 days.

Work done by A and B together in the last 4 days = 4 (1/24 + 1/30) = 3/10.

Remaining Work = 7/10, which was done by A,B and C in the initial number of days.

Number of days required for this initial work = 7 days.

Thus, the total numbers of days required = 4 + 7 = 11 days.

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A can do a piece of work in 10 days, B in 15 days. They work together for 5 days, the rest of the work is finished by C in two more days. If they get Rs. 3000 as wages for the whole work, what are the daily wages of A, B and C respectively (in Rs):

A's 5 days work = 50%

B's 5 days work = 33.33%

C's 2 days work = 16.66% [100- (50+33.33)]

Ratio of contribution of work of A, B and C = 50 : 33 1 3 : 16 2 3 = 3 : 2 : 1

A's total share = Rs. 1500

B's total share = Rs. 1000

C's total share = Rs. 500

A's one day's earning = Rs.300

B's one day's earning = Rs.200

C's one day's earning = Rs.250

View Answer Report Error Discuss Filed Under: Time and Work Exam Prep: CAT , Bank Exams , AIEEE Job Role: Bank PO , Bank Clerk

P can complete a work in 12 days working 8 hours a day.Q can complete the same work in 8 days working 10 hours a day. If both p and Q work together,working 8 hours a day,in how many days can they complete the work?

P can complete the work in (12 x 8) hrs = 96 hrs

Q can complete the work in (8 x 10) hrs=80 hrs

Therefore, P's 1 hour work=1/96 and Q's 1 hour work= 1/80

(P+Q)'s 1 hour's work =(1/96) + (1/80) = 11/480. So both P and Q will finish the work in 480/11 hrs

Therefore, Number of days of 8 hours each = (480/11) x (1/8) = 60/11

12 men can complete a work in 8 days. 16 women can complete the same work in 12 days. 8 men and 8 women started working and worked for 6 days. How many more men are to be added to complete the remaining work in 1 day?

1 man's 1 day work =1/96 ; 1 woman's 1 day work = 1/192

Work done in 6 days= 6 8 96 + 8 192 = 6 × 1 8 = 3 4

Remaining work = 1/4

(8 men +8 women)'s 1 day work = 1 8 96 + 8 192 =1/8

Remaining work =1/4 - 1/8 = 1/8

1/96 work is done in 1 day by 1 man

Therefore, 1/8 work will be done in 1 day by 96 x (1/8) =12 men

An air conditioner can cool the hall in 40 miutes while another takes 45 minutes to cool under similar conditions. If both air conditioners are switched on at same instance then how long will it take to cool the room approximately ?

Let the two conditioners be A and B

'A' cools at 40min

'B' at 45min

Together = (a x b)/(a + b)

= (45 x 40)/(45 + 40)

= 45 x 40/85

= 22 min (approx).

View Answer Report Error Discuss Filed Under: Time and Work Exam Prep: GRE , GATE , CAT , Bank Exams , AIEEE Job Role: Bank PO , Bank Clerk

Relation Between Efficiency and Time

A is twice as good a workman as B and is therefore able to finish a piece of work in 30 days less than B.In how many days they can complee the whole work; working together?

Ratio of times taken by A and B = 1 : 2.

The time difference is (2 - 1) 1 day while B take 2 days and A takes 1 day.

If difference of time is 1 day, B takes 2 days.

If difference of time is 30 days, B takes 2 x 30 = 60 days.

So, A takes 30 days to do the work.

A's 1 day's work = 1/30

B's 1 day's work = 1/60

(A + B)'s 1 day's work = 1/30 + 1/60 = 1/20

A and B together can do the work in 20 days.

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A,B,C together can do a piece of work in 10 days.All the three started workingat it together and after 4 days,A left.Then,B and C together completed the work in 10 more days.In how many days can complete a work alone ?

(A+B+C) do 1 work in 10 days.

So (A+B+C)'s 1 day work=1/10 and as they work together for 4 days so workdone by them in 4 days=4/10=2/5

Remaining work=1-2/5=3/5

(B+C) take 10 more days to complete 3/5 work. So( B+C)'s 1 day work=3/50

Now A'S 1 day work=(A+B+C)'s 1 day work - (B+C)'s 1 day work=1/10-3/50=1/25

A does 1/25 work in in 1 day

Therefore 1 work in 25 days.

View Answer Report Error Discuss Filed Under: Time and Work Exam Prep: GRE , GATE , CAT , Bank Exams , AIEEE Job Role: Bank PO , Bank Clerk , Analyst

3 men, 4 women and 6 children can complete a work in 7 days. A woman does double the work a man does and a child does half the work a man does. How many women alone can complete this work in 7 days ?

Let 1 woman's 1 day work = x.

Then, 1 man's 1 day work = x/2 and 1 child's 1 day work x/4.

So, (3x/2 + 4x + + 6x/4) = 1/7

28x/4 = 1/7 => x = 1/49

1 woman alone can complete the work in 49 days.

So, to complete the work in 7 days, number of women required = 49/7 = 7.

View Answer Report Error Discuss Filed Under: Time and Work Exam Prep: AIEEE , Bank Exams , CAT , GATE Job Role: Bank Clerk , Bank PO

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Study Material

LCM METHOD FOR TIME AND WORK PROBLEMS

In this section, you will learn how to solve time and work problems using least common multiple.

Let us look at the steps involved in solving time and work problems using least common multiple.

Find the least common multiple for all the given days / hours / minutes.

Least common multiple found in step 1 is considered as total amount of work to be completed.

Use the formula given below to solve the problem.

Further process from step 3 will be depending upon the situation given in the problem.

It has been explained clearly in the examples given below.

Example 1 :

A can do a piece of work in 8 days. B can do the same in 14 days. In how many days can the work be completed if A and B work together?

Let us find LCM for the given no. of days 8 and 14.

L.C.M of (8, 14) is 56.

Therefore, the total work is 56 units.

A can do = ⁵⁶⁄₈ = 7 units/day

B can do = ⁵⁶⁄₁₄ = 4 units/day

(A + B) can do = 11 units per day

So, no. of days taken by (A + B) to complete the same work is

= ⁵⁶⁄₁₁ days

Example 2 :

A and B together can do a piece of work in 12 days and A alone can complete the work in 21 days. How long will B alone to complete the same work?

Let us find LCM for the given no. of days 12 and 21.

L.C.M of (12, 21) is 84.

Therefore, the total work is 84 units.

A can do = ⁸⁴⁄₂₁ = 4 units/day

(A + B) can do = ⁸⁴⁄₁₂ = 7 units/day

B can do = (A + B) - A = 7 - 4 = 3 units/day

So, no. of days taken by B alone to complete the same work is

Example 3 :

A and B together can do a piece of work in 110 days. B and C can do it in 99 days. C and A can do the same work in 90 days. How long would each take to complete the work?

Let us find LCM for the given no. of days 110, 99 and 90.

L.C.M of (110, 99, 90) is 990.

Therefore, the total work is 990 units.

A + B = ⁹⁹⁰⁄₁₁₀ = 9 units/day ---->(1)

B + C = ⁹⁹⁰⁄₉₉ = 10 units/day ---->(2)

A + C = ⁹⁹⁰⁄₉₀ = 11 units/day ---->(3)

By adding (1), (2) & (3), we get,

2A + 2B + 2C = 30 units/day

2(A + B + C) = 30 units/day

A + B + C = 15 units/day ---->(4)

(4) - (1) ----> (A + B + C) - (A + B) = 15 - 9 = 6 units

C can do = 6 units/day

C will take = ⁹⁹⁰⁄₆ = 165 days

(4) - (2) ----> (A + B + C) - (B + C) = 15 - 10 = 5 units

A can do = 5 units/day

A will take = ⁹⁹⁰⁄₅ = 198 days

(4) - (3) ----> (A + B + C) - (A + C) = 15 - 11 = 4 units

Therefore B can do 4 units per day.

So, the number of days taken by B to complete the work is

= 247.5 days

Example 4 :

A and B can do a work in 15 days. B and C can do it in 30 days. C and A can do the same work in 18 days. They all work together for 9 days and then A left. In how many days can B and C finish remaining work?

Let us find LCM for the given no. of days 15, 30 and 18.

L.C.M of (15, 30, 18) is 90 units.

Therefore, the total work is 90 units.

A + B = ⁹⁰⁄₁₅ = 6 units/day ---->(1)

B + C = ⁹⁰⁄₃₀ = 3 units/day ---->(2)

A + C = ⁹⁰⁄₁₈ = 5 units/day ---->(3)

2A + 2B + 2C = 14 units/day

2(A + B + C) = 14 units/day

A + B + C = 7 units/day ---->(4)

A, B and C all work together for 9 days.

No. of units completed in these 9 days is

= 7 ⋅ 9

Remaining work to be completed by B and C is

So, no. of days taken by B and C to complete the work is

[Because (B + C) = 3 units/day]

Example 5 :

A and B each working alone can do a work in 20 days and 15 days respectively. They started the work together, but B left after sometime and A finished the remaining work in 6 days. After how many days from the start, did B leave?

Let us find LCM for the given no. of days 20 and 15.

L.C.M of (20, 15) is 60 units.

Therefore, the total work is 60 units.

A can do = ⁶⁰⁄₂₀ = 3 units/day

B can do = ⁶⁰⁄₁₅ = 4 units/day

(A + B) can do = 7 units/day

The work done by A alone in 6 days is

= 6 ⋅ 3

Then the work done by (A + B) is

So, initially no. of days worked by A and B together is

Example 6 :

A is 3 times as fast as B and is able to complete the work in 30 days less than B. Find the time in which they can complete the work together.

A and B working capability ratio is 3 : 1.

Then, A and B time taken ratio is 1 : 3.

From the ratio,

Time taken by A = k

Time taken by B = 3k

Given : A takes 30 days less than B.

Then, we have

3k - k = 30

time taken by A = 15 days

time taken by B = 3 ⋅ 15 = 45 days

LCM (15, 45) is 45.

Total work is 45 units.

A can do = ⁴⁵⁄₁₅ = 3 units/day

B can do = ⁴⁵⁄₄₅ = 1 unit/day

(A + B) can do = 4 units per day

So, no. of days taken by (A + B) to complete the same work is

= 11 ¼ days

Example 7 :

A and B working separately can do a piece of work in 10 and 8 days respectively. They work on alternate days starting with A on the first day. In how many days will the work be completed?

Let us find LCM of the given no. of days 10 and 8.

LCM of (10, 8) is 40.

Total work is 40 units.

A can do = ⁴⁰⁄₁₀ = 4 units/day

B can do = ⁴⁰⁄₈ = 5 units/day

On the first two days,

A can do 4 units on the first day and B can do 5 units on the second day.

(Because they are working on alternate days)

Total units completed in the 1st day and 2nd day is

= 9 units ----(1)

Total units completed in the 3rd day and 4th day is

= 9 units ----(2)

Total units completed in the 5th day and 6th day is

= 9 units ----(3)

Total units completed in the 7th day and 8th day is

= 9 units ----(4)

By adding (1),(2),(3) & (4), we get 36 units.

That is, in 8 days 36 units of the work completed.

Remaining work is

These units will be completed by A on the 9th day.

So, the work will be completed in 9 days.

Example 8 :

Two pipes A and B can fill a tank in 16 minutes and 20 minutes respectively. If both the pipes are opened simultaneously, how long will it take to complete fill the tank?

Let us find LCM of the given no. of minutes 16 and 20.

LCM of (16, 20) is 80.

Total work is 80 units.

A can fill = ⁸⁰⁄₁₆ = 5 units/min

B can fill = ⁸⁰⁄₂₀ = 4 units/min

(A + B) can fill = 9 units/min

So, no. of minutes taken by (A + B) to fill the tank is

= 8 ⁸⁄₉ minutes

Example 9 :

Pipe A can fill a tank in 10 minutes. Pipe B can fill the same tank in 6 minutes. Pipe C can empty the tank in 12 minutes. If all of them work together, find the time taken to fill the empty tank.

Let us find LCM of the given no. of minutes 10, 6 and 12.

LCM of (10, 6, 12) is 60.

Total work is 60 units.

A can fill = ⁶⁰⁄₁₀ = 6 units/min

B can fill = ⁶⁰⁄₆ = 10 units/min

(A + B) can fill = 16 units/min

C can empty = ⁶⁰⁄₁₂ = 5 units/min

If all of them work together,

(6 + 10 - 5) = 11 units/min will be filled

If all of them work together, time taken to fill the empty tank is

= 5 ⁵⁄₁₁ minutes

Example 10 :

A water tank is two-fifth full. Pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely?

Let us find LCM of the given no. of minutes 10 and 6.

LCM of (10, 6) is 30.

Total work is 30 units (to fill the empty tank).

Already tank is two-fifth full.

So, the work completed already is

= ( ⅖ ) ⋅ 30

Out of 30 units, now the tank is 12 units full.

A can fill = ³⁰⁄₁₀ = 3 units/min

B can empty = ³⁰⁄₆ = 5 units/min

If both the pipes are open, the tank will be emptied in

= 2 units/minute

The t ank is already two-fifth full (12 units).

So, no. of minutes taken to empty the tank is

= 6 minutes

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Work-related Problems

Case 1: Workers have different rates

Work rate = (1 job done) / (Time to finish the job)

Time of doing the job = (1 job done) / (Work rate)

For example Albert can finish a job in A days Bryan can finish the same job in B days Carlo can undo the job in C days

1/A = rate of Albert 1/B = rate of Bryan -1/C = rate of Carlo

Albert and Bryan work together until the job is done: (1/A + 1/B)t = 1 Albert is doing the job while Carlo is undoing it until the job is done: (1/A - 1/C)t = 1

Problem Lejon can finish a job in 6 hours while Romel can do the same job in 3 hours. Working together, how many hours can they finish the job?

$(1/6 + 1/3)t = 1$

$\frac{1}{2}t = 1$

$t = 2 \, \text{ hours}$ answer

Case 2: Workers have equal rates

Work done = no. of workers × time of doing the job

To finish the job

If a job can be done by 10 workers in 5 hours, the work load is 10(5) = 50 man-hours. If 4 workers is doing the job for 6 hours, the work done is 4(6) = 24 man-hours. A remaining of 50 - 24 = 26 man-hours of work still needs to be done.

Problem Eleven men could finish the job in 15 days. Five men started the job and four men were added at the beginning of the sixth day. How many days will it take them to finish the job?

Let $x$ = no. of days for them to finish the job $25 + (5 + 4)(x - 5) = 165$

$25 + 9(x - 5) = 165$

$x = 20.56 \, \text{ days}$ answer

A tank is supplied by two pipes A and B and emptied by a third pipe C
Number of Hours for Pipe to Fill the Tank if the Drain is Closed
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7 Everyday Work Problems AI Helps Me Solve

A s we all constantly hear, AI is poised to change everything forever—it will replace workers, create new drugs, maybe destroy the world.

But for the moment, I’m more excited about the ways AI already can fix the annoying, day-to-day problems that plague my working life.

I can get help if I zone out during a meeting, need to write a diplomatic note to an irksome colleague or want tech help ASAP. These aren’t exactly the world-shaking problems that AI promises to solve, but they are the kinds of things that frustrate us constantly.

Here are seven of the biggest problems AI tools have already solved for me.

I lost track of a meeting.

Sometimes the ping of an incoming message or the tedium of back-to-back video calls means I lose track of what is happening in a meeting. This is when an AI meeting assistant comes in handy. These tools transcribe, recap and organize what happens in a meeting so you get a tidy summary with action items afterward. Some assistants (like the transcription built into Zoom and Teams, or the add-on app from Otter.ai) even transcribe in real time, so you can quickly scroll back through the conversation.

I’m overwhelmed by email.

The job of managing email has become dramatically easier thanks to a new generation of email clients that use AI to triage the incoming flood and expedite the job of responding. AI-enhanced email programs like Superhuman and Shortwave can analyze the content of your messages and keep track of different senders, allowing them to organize your inbox by message type and priority (so all your sales newsletters get grouped together, say, and don’t clutter up your main inbox). The programs can also draft message replies.

Using an AI-enabled email client keeps my primary inbox to just the most important messages, so I don’t fall behind or get overwhelmed; I look at everything else (my newsletters and my “other” pile) when I have time.

I have to deal with an annoying colleague.

Sometimes I get so annoyed with an uncooperative, argumentative or condescending colleague that I can’t resist writing a very sharp, hostile email. I used to give myself a 24-hour cooling-off period before sending those draft messages, and then give them to my husband to review and edit. Now, I give the same job to an AI.

If I tell the AI something like, “Please rewrite this email reply so that it is constructive and cordial, rather than hostile,” I get a fresh perspective on how to reframe my snappy comebacks. That is how I learned to say, “During the past weeks, aligning directly was challenging,” rather than, “It is super frustrating that I couldn’t get any time from you.” I still get the emotional satisfaction of being as direct as I want, but the AI smooths off my edges and turns the draft into a message that can actually get the outcome I want.

I need tech support.

A day rarely goes by without needing some kind of tech support—such as learning how to use a new app or troubleshooting glitches with a videoconferencing platform. But I hate watching how-to videos, and I don’t always have time to read through an online manual or to call a manufacturer. Now I just ask Perplexity or ChatGPT how to solve my problem. That way I get step-by-step instructions that are tailored to my particular level of expertise, and I can ask clarifying questions if I get confused or if my initial steps didn’t work.

I don’t understand the subject.

If I need to read up on an academic or technical subject that is totally new to me, I often ask a general-purpose AI (like Claude, Perplexity or ChatGPT) to give me a broad summary of the field, or I use an AI-enabled academic-research tool like scite to give me a summary of the top insights in the field. But that is just a starting point, because AIs often base their summaries on a quirky subset of the academic literature, or they outright make things up. Once I have my bearings, I pick a few credible articles (ones with a lot of citations, or which have been recommended by experts) and get an AI to summarize them and clarify any points I don’t understand.

I hate doing tedious work.

I have yet to find a job that doesn’t involve some amount of tedious work—whether it is invoicing, proofreading, data cleaning or file organizing. Now I give just about all my boring and annoying tasks to an AI. For example, I have a supplier who gives me invoices in a form my accounting system won’t accept; rather than redoing those invoices by hand (or asking my nontechie supplier to fix them), I use AI to do the work for me.

It took all of five minutes to come up with the prompt that does the job: “You are a billing agent for a supplier. Your main role is to take rough billing notes and organize them into a structured table. The table should have columns for date, time period and hours worked, with one row a day. Your goal is to provide clear and accurate billing information, ensuring that all details are neatly organized and easily understandable.”

Once I have that prompt, I can use it over and over. Now all I do is paste my supplier’s latest invoice after that prompt, and I get back a table I can slap into Excel and send to my bookkeeping app.

I need more examples.

When I’m working on an article, presentation or report, I’m often stuck for just the right example to make it complete—which can mean searching the internet for hours or asking friends and colleagues to share their own examples and experiences. But now I just ask a web-enabled AI like Perplexity for something like “five examples of manufacturing companies that have embraced hybrid work.” Or I ask a couple of different AIs to help me brainstorm more examples for a work in progress—like feeding Claude and ChatGPT a draft of the first six problems in this article, and asking them to suggest more problems AI might be able to solve.

When I did that, the AIs fed me a list that reminded me of many other ways AI has removed big pain points from my working life. “Finding relevant information in a sea of data”: Yes, I often upload spreadsheets to AIs and ask them for help reorganizing or surfacing patterns. “Enhancing creative brainstorming”: True, AI has removed the bottleneck of needing a sounding board for my new ideas, because now I can always turn to an AI as my virtual sounding board. “Enhancing social-media management”: Just as ChatGPT suggested, I have used AI to analyze the performance of online posts and figure out the best hooks and titles for future updates.

The list went on and on, in a beautiful illustration of what makes AI solutions so powerful: AI can not only address our working pain points, but also retains a memory of everything it’s fixed, long after my human memory forgets what it was like to work in any other way.

Alexandra Samuel is a technology researcher and co-author of “Remote, Inc.: How to Thrive at Work…Wherever You Are.” She can be reached at [email protected].

7 Everyday Work Problems AI Helps Me Solve

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May 10, 2024 • 27:42 Stormy Daniels Takes the Stand
May 9, 2024 • 34:42 One Strongman, One Billion Voters, and the Future of India
May 8, 2024 • 28:28 A Plan to Remake the Middle East
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May 6, 2024 • 29:23 R.F.K. Jr.’s Battle to Get on the Ballot
May 3, 2024 • 25:33 The Protesters and the President
May 2, 2024 • 29:13 Biden Loosens Up on Weed
May 1, 2024 • 35:16 The New Abortion Fight Before the Supreme Court
April 30, 2024 • 27:40 The Secret Push That Could Ban TikTok
April 29, 2024 • 47:53 Trump 2.0: What a Second Trump Presidency Would Bring
April 26, 2024 • 21:50 Harvey Weinstein Conviction Thrown Out
April 25, 2024 • 40:33 The Crackdown on Student Protesters

Stormy Daniels Takes the Stand

The porn star testified for eight hours at donald trump’s hush-money trial. this is how it went..

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This episode contains descriptions of an alleged sexual liaison.

What happened when Stormy Daniels took the stand for eight hours in the first criminal trial of former President Donald J. Trump?

Jonah Bromwich, one of the lead reporters covering the trial for The Times, was in the room.

On today’s episode

Jonah E. Bromwich , who covers criminal justice in New York for The New York Times.

A woman is walking down some stairs. She is wearing a black suit. Behind her stands a man wearing a uniform.

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In a second day of cross-examination, Stormy Daniels resisted the implication she had tried to shake down Donald J. Trump by selling her story of a sexual liaison.

Here are six takeaways from Ms. Daniels’s earlier testimony.

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Jonah E. Bromwich covers criminal justice in New York, with a focus on the Manhattan district attorney’s office and state criminal courts in Manhattan. More about Jonah E. Bromwich

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Industrial Design Case Study: A Package Management System

Formation design group tackles hellopackage.

These days an ID firm might be called on to design a system, rather than a product. Package Solutions is a company seeking to solve the problems of delivering packages to multi-resident buildings and student housing. They hired Formation Design Group to work out the solutions.

"The rapid growth of e-commerce has overwhelmed last mile package delivery, particularly in multifamily residential communities," the firm writes. "Formation worked with Package Solutions to streamline their user experience and commercialize their cutting edge package tracking technology."

Beyond the Room

Using contextual research as a basis, Formation conceptualized a multitude of mobile application features to improve resident experience, create opportunities for additional revenue and provide new amenities. The mobile application empowers residents, carriers, and staff to interact with the HelloPackage system while away from the community. Beyond package delivery, the system engages with residents to provide useful features that fit seamlessly into the rhythm of life in a multifamily community.

Creating Community

Using the HelloPackage app residents can send, receive, transfer or redirect their packages. The system allows trusted roommates, neighbors and staff to retrieve packages for each other and rewards them with points redeemable for merchandise stored on secured shelves and other benefits. Features like these build community, increase package throughput, and ultimately allow people to get their stuff in the way that works best for them.

An Adaptable Platform

HelloPackage's hardware was designed to be minimal, attractive and adaptable. The system is based on a simple kit of parts that can be combined to adapt to any space. The system can be easily expanded to scale with a community's needs. Sheet metal construction provides an efficient, durable platform with limitless design and aesthetic possibilities.

This integrated hardware/software system makes managing packages easier for community staff, carriers and ultimately for the resident/recipient.

The solution is a powerful combination of software & hardware that revolutionizes the package delivery experience for apartment staff, residents and carriers.

You can see more of Formation's work here .

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IMAGES

How to Solve Work and days problems
How to solve Time and Work problems in simpler steps, type 2 brief
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Time and Work ( LCM Method)

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कार्य एवं दूरी || work & Time important question || for upsc cast,SSC, Railway, police, PSC all exam
Time And Work Trending Questions #previousyearsquestions #mathsbydeepakpanchalsir #sscmaths#sscexam
Mathematics Work Problems With Solutions || HEC ETC, FPSC, PPSC, NTS CTSP ||
Solve Rational Equations for Work related Application problems
TN Class 8 Maths Life Mathematics Example 4.23 Time & Work /Tnpsc Aptitude Time and Work problems
A and B can do a work in 12 days,B and C can do it in 15 days and C and A can do it in 20 days

COMMENTS

Time and Work Problems
FORMULAS. The basic formula for solving is: 1/r + 1/s = 1/h. Let us take a case, say a person Hrithik. Let us say that in 1 day Hrithik will do 1/20 th of the work and 1 day Dhoni will do 1/30 th of the work. Now if they are working together they will be doing 1/20 + 1/30 = 5/60 = 1/12 th of the work in 1 day. Now try to analyze, if two persons ...
Time and Work
Given below are a few such important time and work formulas for your reference: Work Done = Time Taken × Rate of Work. Rate of Work = 1 / Time Taken. Time Taken = 1 / Rate of Work. If a piece of work is done in x number of days, then the work done in one day = 1/x. Total Wok Done = Number of Days × Efficiency.
Time and Work Problems
This math video tutorial focuses on solving work and time problems using simple tricks and shortcuts. It contains a simple formula that you can use with the...
Time and Work Problems
TIME AND WORK PROBLEMS. 1. If a person can do a piece of work in 'm' days, he can do ¹⁄m part of the work in 1 day. 2. If the number of persons engaged to do a piece of work be increased (or decreased) in a certain ratio the time required to do the same work will be decreased (or increased) in the same ratio. 3.
9.10 Rate Word Problems: Work and Time
For Questions 9 to 20, find and solve the equation describing the relationship. If an apprentice can do a piece of work in 24 days, and apprentice and instructor together can do it in 6 days, how long would it take the instructor to do the work alone? A carpenter and his assistant can do a piece of work in 3.75 days.
Algebra Work Problems (solutions, examples, videos)
Work Problems: word problems involving rates of work solve using algebra, work problems with pipes filling up a tank, work problems with one unknown time and work problems with pumps draining a tank, examples with step by step solutions ... If the first painter starts and 3 days later the coworker joins in to help finish the job, how many days ...
How to Solve Work and Time Problems
Time and work are related with the time taken by a person or a group of persons to complete a task and the efficiency of the work done by each of them. Here we have provided detailed information about how to solve work and time problems. Step 1: To find one day work. If A can do a piece of work in 10 days, then A's one day work will be 1/10.
Math Work Problems (video lessons, examples and solutions)
Solution: Step 1: Assign variables: Let x = time to mow lawn together. Step 2: Use the formula: Step 3: Solve the equation. The LCM of 40 and 60 is 120. Multiply both sides with 120. Answer: The time taken for both of them to mow the lawn together is 24 minutes.
Time and Work Concepts, Tricks and Formulas
Let us assume A alone completes the work in x days and B alone completes the work in 3x days. 3x = 12. x = 4. Therefore, A alone can complete the work in 4 days. Note: The concept of efficiency is widely used to equate the works of men, women, and children. Let us understand the application of the concept of efficiency through a question
Problems on Time and Work
Now we will learn how to use the concept of time and work for solving various problems. Word problems on time and work: 1. Adam is thrice as good a workman as Brain and together they finish the piece of work in 15 days. In how many days will Adam alone finish the work? Solution: Adam's 1 day's work: Brain's 1 day's work = 3 : 1.
"Work" Word Problems
As you can see in the above example, "work" problems commonly create rational equations. But the equations themselves are usually pretty simple to solve. One pipe can fill a pool 1.25 times as fast as a second pipe. When both pipes are opened, they fill the pool in five hours.
3 Ways to Solve Combined Labor Problems
4) Set up the equation and solve the equation h/x = y, where h equals the amount of days it will take the remaining person to complete the job, x equals the amount of days it takes that person to complete the job on his own, and y equals the amount of work that still needs to be done. Thanks!
Time & Work
Q 3 - A can do a bit of work in 25 days which B can complete in 20 days. Both together labor for 5 days and afterward A leaves off. How long will B take to complete the remaining work? A - 7 days. B - 8 days. C - 9 days. D - 11 days
Work from Days: Concepts, Examples and Practice Questions
This means, in one day A and B together can do 30% of work. Therefore, the number of days it will take A and B together to do 100% of the work = 100/30 = 3.33 days. Some Solved Examples. Example 4: A and B can do a job in 8 days. B and C can do the same job in 12 days. When A, B, and C work together, they can do the same job in 6 days.
Formulas For Work And Time
Answer: Let the amount of work required for the project be represented as "1 project.". Time taken by 6 workers to complete the work in = 18 days. Let there be X workers to complete the same work in 9 days. X = \frac {6 \times 18} {9} X = 6 \times 2. X = 12 workers.
Work Problems: Basic Concepts
Individual Rates versus Combined Rates. In a two-person work problem, there are always three rates involved: the rate the job is done when the first person works alone; the rate the job is done when the second person works alone; the rate the job is done when both people work together; The first two rates are called the individual rates, and the last one is called the combined rate.
Work Word Problems (video lessons, examples, solutions)
Algebra Work Problems: word problems involving rates of work, how to solve work problems that involve two persons, more than two persons, pipes filling up a tank, with video lessons, examples and step-by-step solutions. ... Pipe 1 takes 5 days to drain a pool and pipe 2 takes 7 days to drain the pool. How long will it take for the two pipes to ...
Time and Work
Exercise : Time and Work - General Questions. 1. A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is : 2. A can lay railway track between two given stations in 16 days and B can do the same job in 12 days. With help of C, they did the job in 4 days only.
420+ Solved Time and Work Problems with Solutions and Explanation
Job Role: Bank Clerk , Bank PO. 84 37503. Frequently asked time and work questions or problems with solutions, shortcuts, formulas for all important competitive exams like bank, interviews. Learn and free practice on fully solved time and work aptitude questions, useful tips to be top in exams.
LCM METHOD FOR TIME AND WORK PROBLEMS
Step 1 : Find the least common multiple for all the given days / hours / minutes. Step 2 : Least common multiple found in step 1 is considered as total amount of work to be completed. Step 3 : Use the formula given below to solve the problem. Further process from step 3 will be depending upon the situation given in the problem.
Work-related Problems
Work-related Problems. Case 1: Workers have different rates. Work rate × Time to finish the job = 1 job done. Work rate = (1 job done) / (Time to finish the job) Time of doing the job = (1 job done) / (Work rate) For example. Albert can finish a job in A days. Bryan can finish the same job in B days. Carlo can undo the job in C days.
Work Problems
Work problems are those that involve the speeds of people and/or machines. We will teach you how to calculate how long it will take for multiple workers to perform a job. This lesson is broken down into three sections: Rationale for Learning Work Problems. Work Basics. Solving Simple Rational Equations.
How to Solve Problems at Work: A Step-by-Step Guide
Step 3: Identify the source of the issue. Beyond defining the problem that you're faced with, you may also need to identify the root of the problem. This will guide you towards a solution that not only fixes the problem that lies at the surface but also resolve a far deeper issue that could cause more problems to arise in the future.
7 Everyday Work Problems AI Helps Me Solve
7 Everyday Work Problems AI Helps Me Solve. As we all constantly hear, AI is poised to change everything forever—it will replace workers, create new drugs, maybe destroy the world. But for the ...
Stormy Daniels Takes the Stand
On today's episode. Jonah E. Bromwich, who covers criminal justice in New York for The New York Times. Stormy Daniels leaving court on Thursday, after a second day of cross-examination in the ...
Seven Common Work Problems AI Helps Me Solve
7 Everyday Work Problems AI Helps Me Solve ... But for the moment, I'm more excited about the ways AI already can fix the annoying, day-to-day problems that plague my working life.
Industrial Design Case Study: A Package Management System
These days an ID firm might be called on to design a system, rather than a product. Package Solutions is a company seeking to solve the problems of delivering packages to multi-resident buildings and student housing. They hired Formation Design Group to work out the solutions. "The rapid growth of e-commerce has overwhelmed last mile package delivery, particularly in multifamily residential ...

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Step 1: To find one day work

Step 2: Work and Wages

Step 3: To find the Ratio

Step 4: To Find Efficiency

Step 5: number of days required to complete the work by A and B

Step 6: Know the Important Time and Work Formulas

Step 7: Practice Time and Work Questions

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