time problem solving

20 Elapsed Time Word Problems

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Elapsed time is the amount of time that passes between the beginning and the end of an event. The concept of elapsed time fits nicely in the elementary school curriculum. Beginning in third grade, students should be able to tell and write time to the nearest minute and solve word problems involving addition and subtraction of time. Reinforce these essential skills with the following elapsed time word problems and games.

Elapsed Time Word Problems

These quick and easy elapsed time word problems are perfect for parents and teachers who want to help students practice elapsed time to the nearest minute with simple mental math problems. Answers are listed below.

• Sam and his mom arrive at the doctor’s office at 2:30 p.m. They see the doctor at 3:10 p.m. How long was their wait?
• Dad says dinner will be ready in 35 minutes. It’s 5:30 p.m. now. What time will dinner be ready?
• Becky is meeting her friend at the library at 12:45 p.m. It takes her 25 minutes to get to the library. What time will she need to leave her house to arrive on time?
• Ethan’s birthday party started at 4:30 p.m. The last guest left at 6:32 p.m. How long did Ethan’s party last?
• Kayla put cupcakes in the oven at 3:41 p.m. The directions say that the cupcakes need to bake for 38 minutes. What time will Kayla need to take them out of the oven?
• Dakota arrived at school at 7:59 a.m. He left at 2:33 p.m. How long was Dakota at school?
• Dylan started working on homework at 5:45 p.m. It took him 1 hour and 57 minutes to complete it. What time did Dylan complete his homework?
• Dad arrives home at 4:50 p.m. He left work 40 minutes ago. What time did Dad get off work? 
• Jessica’s family is traveling from Atlanta, Georgia to New York by plane. Their flight leaves at 11:15 a.m. and should take 2 hours and 15 minutes. What time will their plane arrive in New York?
• Jordan got to football practice at 7:05 p.m. Steve showed up 11 minutes later. What time did Steve get to practice?
• Jack ran a marathon in 2 hours and 17 minutes. He crossed the finish line at 10:33 a.m. What time did the race start?
• Marci was babysitting for her cousin. Her cousin was gone for 3 hours and 40 minutes. Marci left at 9:57 p.m. What time did she start babysitting? 
• Caleb and his friends went to see a movie at 7:35 p.m. They left at 10:05 p.m. How long was the movie?
• Francine got to work at 8:10 a.m. She left at 3:45 p.m. How long did Francine work?
• Brandon went to bed at 9:15 p.m. It took him 23 minutes to fall asleep. What time did Brandon fall asleep?
• Kelli had to wait in a long, slow-moving line to purchase a popular new video game that was just released. She got in line at 9:15 a.m. She left with the game at 11:07 a.m. How long did Kelli wait in line?
• Jaydon went to batting practice Saturday morning at 8:30 a.m. He left at 11:42 a.m. How long was he at batting practice?
• Ashton got behind on her reading assignment, so she had to read four chapters last night. She started at 8:05 p.m. and finished at 9:15 p.m. How long did it take Ashton to catch up on her assignment?
• Natasha has a dentist appointment at 10:40 a.m. It should last 35 minutes. What time will she finish?
• Mrs. Kennedy’s 3rd-grade class is going to the aquarium on a field trip. They are scheduled to arrive at 9:10 a.m. and leave at 1:40 p.m. How long will they spend at the aquarium?

Elapsed Time Games

Try these games and activities at home to help your children practice elapsed time.

Daily Schedule

Let your children keep track of their schedule and ask them to figure the elapsed time for each activity. For example, how long did your child spend eating breakfast, reading, taking a bath, or playing video games?

How Long Will It Take?

Give your kids practice with elapsed time by encouraging them to figure out how long daily activities take. For example, the next time you order a pizza online or by phone, you'll probably be given an estimated delivery time. Use that information to create a word problem that's relevant to your child's life, such as, "It's 5:40 p.m. now and the pizza shop says the pizza will be here at 6:20 p.m. How long will it take for the pizza to arrive?"

Order a set of time dice from online retailers or teacher supply stores. The set contains two twelve-sided dice, one with numbers representing the hours and the other with numbers representing minutes. Take turns rolling the time dice with your child. Each player should roll twice, then calculate the elapsed time between the two resulting dice times. (A pencil and paper will come in handy, as you'll want to jot down the time of the first roll.)

Elapsed Time Word Problem Answers

•  2 hours and 2 minutes
• 6 hours and 34 minutes
• 2 hours and 30 minutes
• 7 hours and 35 minutes
• 1 hour and 52 minutes
• 3 hours and 12 minutes
• 1 hour and 10 minutes
• 4 hours and 30 minutes
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• How To Tell Time in Spanish
• Sinking of the RMS Titanic
• A Timeline of the Sinking of the Titanic
• How to Tell Time in Italian
• When Is the Spring Equinox?
• Free Math Word Problem Worksheets for Fifth-Graders
• What Time Is the SAT Test?
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• Proportions Word Problems Worksheet: Answers and Explanations
• Telling Time in French
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25 Time Word Problems for Year 2 to Year 6 With Tips On Supporting Pupils’ Progress

Emma Johnson

Time word problems are an important element of teaching children how to tell the time. Children are introduced to the concept of time in Year 1. At this early stage, they learn the basics of analogue time; reading to the hour and half past and learn how to draw hands on the clocks to show these times.

As they move through primary school, pupils progress onto reading the time in analogue, digital and 24 hour clocks and being able to compare the duration of events. By the time children reach upper Key Stage 2, they should be confident in reading the time in all formats and solving problems involving converting between units of time.

Time in Year 1

Time in year 2, time in year 3, time in year 4, time in year 5 & 6.

• Why are word problems important for children’s understanding of time

How to teach time word problem solving in primary school

Time word problems for year 2, time word problems for year 3, time word problems for year 4, time word problems for year 5, time word problems for year 6, more time and word problems resources.

Let's Practice Telling The Time

Download this free printable worksheet to let your students practice telling the time.

When students are first introduced to time and time word problems , it is important for them to have physical clocks, to hold and manipulate the hands. Pictures on worksheets are helpful, but physical clocks enable them to work out what is happening with the hands and to solve word problems involving addition word problems and subtraction word problems .

Time word problems are important for helping children to understand how time is used in the real-world. We have put together a collection of 25 time word problems, which can be used with pupils from Year 2 to Year 6.

Time word problems in the National Curriculum  

In Year 1, students are introduced to the basics of time. They learn to recognise the hour and minute hand and use this to help read the time to the hour and half past the hour. They also draw hands on clock faces to represent these times. 

By the end of Year 2, pupils should be able to tell the time to five minutes, including quarter past/to the hour and draw the hands on a clock face to show these times. They should also know the number of minutes in an hour and the number of hours in a day.

In Year 3, children read the time in analogue (including using Roman Numerals). By this stage they are also learning to read digital time in 12 and 24 hour clock, using the AM and PM suffixes. Pupils record and compare time in terms of seconds, minutes and hours; know the number of seconds in a minute, days in a month and year and compare durations of events.

By Year 4, pupils should be confident telling the time in analogue to the nearest minute, digital and 24 hour clock. They also need to be able to read, write and convert time between analogue and digital 12 and 24 hour clocks and solve problems involving converting from hours to minutes; minutes to seconds; years to months and weeks to days. 

By Year 5 and 6, there is only limited mention of time in the curriculum. Pupils continue to build on the knowledge they have picked up so far and should be confident telling the time and solving a range of problems, including: converting units of time; elapsed time word problems, working with timetables and tackling multi-step word problems .

Time word problems have been known to appear on Year 6 SATs tests. Third Space Learning’s online one-to-one SATs revision programme incorporates a wide range of word problems to develop students’ problem solving skills and prepare them the SATs tests. Available for all primary year groups as well as Year 7 and GCSE, our online tuition programmes are personalised to suit the needs of each individual student, fill learning gaps and build confidence in maths.

Why are word problems important for children’s understanding of time

Word problems are important for helping children to develop their understanding of time and the different ways time is used on an every-day basis. Confidence in telling the time and solving a range of time problems is a key life skill. Time word problems provide children with the opportunity to build on the skills they have picked up and apply them to real-world situations.

It’s important children learn the skills needed to solve word problems. Key things they need to remember are: to make sure they read the question carefully; to think whether they have fully understood what is being asked and then identify what they will need to do to solve the problem and whether there are any concrete resources or pictorial representations which will help them.

Here is an example:

Mr Arrowsmith drives to Birmingham. He sets off at 3:15pm. He stops for a break of 15 minutes at 4:50 and arrives in Birmingham at 6:15pm.

How long did Mr Arrowsmith spend driving?

How to solve:

What do you already know?

• We know that he set off at 3:15pm and stopped for a break at 4:50. We can calculate how long the first part of his journey was, by counting on from 3:15 to 4:50.
• He had a break at 4:50pm for 15 minutes, so we won’t include that in our driving time calculation.
• He then must have set off again at 5:05pm, before arriving at 6:15pm. We can use this information to work out the length of the second part of his journey.
• We can then add the 2 journey times together, to calculate the total amount of time spent driving. 

How can this be represented pictorially?

•  We can use a number line to calculate the length of time each journey takes.
• If we start by adding on an hour, we can then calculate how many more minutes for each section of the journey.
• Once we have calculated the journey time for each part of the journey, we can add these together to calculate the total journey time.

Time word problems in Year 2 require students to read the time to o’clock and half past the hour and compare and sequence time intervals. 

Oliver went for a bike ride with his friend. 

He left home at 2 o’clock and came home at 4 o’clock.

How long was he out on his bike for?

Answer: 2 hours

Count on from 2 o’ clock to 4 o’clock or subtract 2 from 4.

Mum went shopping at 3 o’clock and got home an hour later.

Draw the time she got home on the clock below.

Tom baked a cake.

The cake was in the oven for one hour. 

If he took the cake out at half past 11, what time did he put the cake in?

Answer: Half past 10

Use an hour from half past 11.

Arlo starts school at 9 o’clock and has his first break at half past 10. 

How long does he have to wait for his first break?

Answer: One and a half hours.

(Use a number line to count on from 9 to half past 10)

The Smith family are going to the beach.

They plan to leave home at 10 o’clock and the journey take two hours.

What time will they arrive at the beach?

Answer: 12 o’clock

(Use a number line to count on 2 hours from 10 o’clock)

With time word problems for year 3 , students build on their understanding of analogue time from Year 2 and also begin to  read the time in  digital (12 and 24 hour clock). Children also need to be able to compare time and durations of events.

Chloe is walking to football training.

She sets off at 8:40am and takes 17 minutes to get there.

What time does she arrive?

Answer: 8:57

(Count on 17 minutes from 8:40 – use a number line if needed)

(Picture of analogue clock with 2:30 showing here)

Maisie says that in 1 hour and 48 minutes it will be 4:28.

Do you agree? Explain how you worked out your answer.

Answer: Maisie is wrong. It will be 4:18. 

This can be worked out by counting on an hour from 2:30 to 3:30 and then another 48 minutes to 4:18.

The Baker family are driving to their campsite. 

They set off at 8:30 am, drive for 2 hours and 15 minutes, then had a 30 minute break. 

If they drive for another 1 hour and 45 minutes, what time do they arrive at the campsite?

Answer: 12:45pm

Use a number line to show what time they arrive at the break. From 8:30, count on 2 hours and 15 minutes to get to 10:45. Add on the 30 minute break. It is now 11:15. They count on another hour and a half  to 12:45

Ahmed looks at his watch and says ‘it is half past 4 in the afternoon’

Jude says that it is 17:30 in a 24 hour clock.

Is Jude correct? Explain your answer.

Answer: Jude is not correct. Half past 4 in the afternoon is 16:30 not 17:30

How many minutes are there in 2 hours and 30 minutes?

Answer: 150 minutes

60 + 60 + 30 = 150

When solving time word problems for year 4 , pupils need to be confident telling time in analogue, and digital, as well as converting between analogue, 12 hour and 24 hour clock. They also begin to solve more challenging problems involving duration of time and converting time.

If there are 60 seconds in 1 minute. How many seconds are there in 8 minutes?

Answer: 480 seconds

60 x 8 = 480 seconds (calculate 6 x 8, then multiply by 10)

Mason played on his VR from 3:35 to 5:25.

How long did he play on his VR?

Answer: 1 hour and 50 minutes.

Count on from 3:35 (using a numberline if needed)

Jamie started his homework at 3:45pm. He finished 43 minutes later.

What time did Jamie finish? Give your answer in 24 hour clock.

Answer: 16:28

Count on 43 minutes from 3:45 (use a number line, if needed) = 4:28. Convert to 24 hour clock.

Chloe and Freya went to the cinema to watch a film. The film started at 2:05pm and lasted for 1 hour and 43 minutes. 

What time did the film end?

Answer: 3:48pm

Count on one hour from 2:05 pm to 3:05pm, then add another 43 minutes – 3:48pm

A family is driving on their holiday.

They drive for 2 hours and 28 minutes, stop for 28 minutes and then drive a further 1 hour and 52 minutes.

If they left at 8:30am, what time did they arrive?

Answer: 1:18pm

2 hours and 28 minutes from 8:30am = 10:58am

10:58am with a 28 minute break = 11:26am

1 hour 52 minute drive from 11:26 am = 1:18pm

With word problems for year 5 , pupils should be confident telling the time in analogue and digital and solving a wider range of time problems including: converting units of time; interpreting and answering questions on timetables and elapsed time.

The sun set at 19:31 and rose again at 6:28. 

How many hours passed between the sun setting and rising again?

Answer: 10 hours and 57 minutes

Count on from 19:31 to 5:31 (10 hours)

Then count on from 5:31 to 6:28 (57 minutes)

A play started at 14:45 and finished at 16:58.

How long was the play?

Answer: 2 hours and 13 minutes

Count on 2 hours from 14:45 to 16:45, then add another 13 minutes to get to 16:58

How many seconds are there in 23 minutes?

Answer: 1380 seconds

Show as column method: 60 x 23 = 1380

Max ran a race in 2 minutes 13 seconds, Oscar ran it in 125 seconds. 

What was the difference in time between Max and Oscar?

Answer: Oscar was 8 seconds faster.

Max – 2 minutes 13 seconds, Oscar – 2 minutes 5 seconds (difference of 8 seconds)

4 children take part in a freestyle swimming relay.

There times were: 

Maisie: 42.8 seconds

Amber 36.3 seconds

Megan 48.7 seconds

Zymal 45.6 seconds

What was the final time for the relay in minutes and seconds?

Answer: 2:53.4

(Show as column method) 42.8 + 36.3 + 48.7 + 45.6 = 173.4 seconds

173.4 seconds = 2:53.4

No new time concepts are taught to pupils in word problems for year 6 . By this stage they are continuing to build confidence and develop skills within the concepts already taught.

Chess: 25 minutes

Basketball: 40 minutes.

Trampolining: 30 minutes

Gymnastics: 50 minutes

Tennis 40 minutes

Tri golf – 45 minutes

Hamza is choosing activities to take part in at his holiday club.

The activities can’t add up to more than 2 hours.

Which 3 activities could he do, which add up to exactly 2 hours?

Answer: Trampolining, gymnastics and tennis: Trampolining: 30 minutes, gymnastics: 50 minutes, tennis: 40 minutes.

5 children took part in a sponsored swim. The children swam for the following lengths of time:

Sam: 27 minutes 37 seconds

Jemma: 33 minutes 29 seconds.

Ben: 23 minutes 18 seconds

Lucy: 41 minutes 57 seconds

Oliver: 39 minutes 21 seconds

Answer: 18 minutes 30 seconds

Longest: Lucy: 41 minutes 57 seconds

Shortest: Ben: 23 minutes 18 seconds.

Difference – count up from 23 minutes 18 seconds to 41 minutes 57 seconds = 18 minutes 39 seconds

What is 6 minutes 47 seconds in seconds?

Answer: 407 minutes

60 x 6 = 360

360 + 47 = 407 minutes

Bethany’s goal is to run round her school running track in under 8 minutes.

She runs it in 440 seconds. Does she achieve her goal? How far above or below the target is she?

Answer: Bethany beats her target by 40 seconds

8 minutes = 8 x 60 = 480 minutes

Lucy’s favourite programme is on TV twice a week for 35 minutes. 

In 6 weeks, how many hours does Lucy spend watching her favourite programme?

Answer: 7 hours

420 minutes = 7 hours

(Show as column method) 35 x 12 = 420 minutes

420 ÷ 60 = 7 

For more time resources, take a look at our collection of printable time worksheets. Third Space Learning also offers a wide collection of word problems covering a range of topics such as place value, decimals and fractions word problems , percentages word problems , division word problems , ratio word problems , addition and subtraction word problems , multiplication word problems , money word problems and other word problem challenge cards.

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Problems on Calculating Time

Here we will learn to solve different types of problems on calculating time.

We know, the formula to find out time = distance/speed

Word problems on calculating time:

1.  A car travel 60 km in 30 minutes. In how much time will it cover 100 km?

Solution:            

Using the unitary method;

Time taken to cover 60 km = 90 minutes

Time taken to cover 1 km = 90/60 minutes

Time taken to cover 100 km = 90/60 × 100 = 150 minutes

Formula of speed = distance/time

= 60 km/(3/2) hr              [given 1 hour 30 min = 1 30/60 = 1 ½ hours

= 3/2 hours]

= 60/1 × 2/3 km/hr = 40 km/hr

Now, using the formula of time = distance/speed = 100 km/40 km/hr = 5/2 hours

= 5/2 × 60 minutes, (Since 1 hour = 60 minutes)

= 150 minutes

2. Victor covers 210 km by car at a speed of 70 km/hr. find the time taken to cover this distance.

Solution:             

70 km is covered in 1 hour.

1 km is covered in 1/70 hours.

210 km is covered in 1/70 × 210 hours = 3 hours

Given: speed = 70 km/hr, distance covered = 210 km

Time taken = Distance/ Speed = 210/70 hours = 3 hours

3. A train covers a distance of 36 km in 15 minutes. Find the time taken by it to cover the same distance if its speed is decreased by 9 km/hr.

Distance covered by train = 36 km

Time taken = 15 minutes = 15/60 hr = ¼ hr.

Therefore speed of train = Distance covered/time taken

                                    = 36/(1/4) km/hr

                                    = 36/1 × 4/1

                                    = 144 km/hr

Reduced speed = 144 – 9 = 135

Therefore, required time = distance covered/speed

                                    = 36/135 × 60 minutes

                                    = 16 minutes

4. A man is walking at a speed of 6 km per hour. After every km, he takes rest for 2 minutes. How much time will it take to cover a distance of 4 km?

Rest time = Number of rests × time of each rest

               = 3 × 2 minutes

               = 6 minutes

Total time to cover 4 km = 4/6 × 60 + 6 minutes

                                     = (40 + 6) minutes

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Time Worksheets Hub Page

Welcome to our Time Worksheets hub page.

Here you will find links to a wide range of free printable worksheets about Time, which will help your child become more confident telling the time, adding and subtracting time amounts, converting time and solving time word problems.

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• This page contains links to other Math webpages where you will find a range of activities and resources.
• If you can't find what you are looking for, try searching the site using the Google search box at the top of each page.

Time Worksheets

Quicklinks to ...

• Telling the Time sheets
• Time Conversion

Time Puzzles

• Time Calculators

Telling the Time Worksheets

Here is our collection of telling the time worksheets for kids.

The following worksheets involve children telling the time with an analogue clock, and matching analogue and digital times.

O'clock and Half-past

Here is our selection of telling the time worksheets for 1st grade.

Using these sheets will help your child to:

• read o'clock and half-past times;
• convert o'clock and half-past times to digital;
• draw clock hands correctly to mark out o'clock and half-past.
• Telling Time Worksheets o'clock and half past

Quarter Past and Quarter To

Here are our collection of clock worksheets for 2nd grade. These sheets cover telling the time for quarter past and quarter to times.

Using these second grade math worksheets will help your child to:

• read quarter past and quarter to times;
• convert analogue to digital times;
• draw clock hands in the correct place for quarter past and quarter to.
• Clock Worksheets - Quarter Past and Quarter To

Telling the Time to 5 minutes

This section contains our 3rd grade time worksheets to help children tell the time in multiples of 5 minutes.

Using the sheets in this section will help your child to:

• tell the time to the nearest 5 minutes;
• become familiar with both digital and analogue times;
• add and subtract time intervals;
• use the words 'past' and 'to' to describe the time correctly.

These 3rd grade time worksheets will help your child become more familiar with telling the time.

• Telling Time to 5 Minutes Worksheets

Telling the Time to 1 minute

This section contains our 4th grade time worksheets to help children tell the time to the nearest minute.

• tell the time to the nearest minute;
• add and subtract time intervals.

These 4th grade time worksheets will help your child become more familiar with telling the time.

• Telling Time Worksheets Grade 4 (1 minute intervals)

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Converting Time

• 24 Hour Clock Conversion Worksheets

On this webpage there is a selection of printable 24 hour (military time) conversion worksheets which will help you learn to convert from 24 hour clock to standard 12 hour time, and from standard time to 24 hour time.

An answer sheet is provided with each sheet and the sheets are graded with the easiest sheets coming with supporting information.

Time Interval Worksheets

These sheets will help you learn to add and subtract hours and minutes from times as well as working out a range of time intervals.

There are also sheets to help you practice adding and subtracting time intervals.

• Add and Subtract Time Worksheets
• Elapsed Time Worksheets

Looking for an extension activity for children who can already tell the time?

Maybe you want an interesting starter activity for your lesson to get the class thinking?

These printable time puzzles will help to get your child thinking about time and solving problems involving time.

They are good at developing an understanding of the language used in time.

• Printable Time Worksheets - Time Puzzles (easier)
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TIME WORD PROBLEMS

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Time word problems helps kids to understand the time and elapsed time concept. 

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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. If A is twice as good a workman as B, then A will take half the time taken by B to do a certain piece of work.

4. Time and work are always in direct proportion.

more work ----> more time

less work ----> less time

5. A takes m days and B takes n days to complete a work.  If they work together, then the formula to find the number of days taken by them to complete the work is

Problem 1 :

A can do a piece of work in 15 days while B can do it in 10 days. How long will they take together to do it?

Using the above formula, if they work together, number of days taken to complete the work is

Problem 2 :

A and B can complete a work in 6 days .  B and C can complete the same work in 8 days. C and A can complete in 12 days. How many days will take for A, B and C combined together to complete the same amount of work ?

From the given information, we can have

(A + B)'s 1 day work = ⅙

(B + C)'s 1 day work = ⅛

(A + C)'s 1 day work = ¹⁄₁₂

(A + B + B + C + A + C)'s 1 day work =  ⅙ + ⅛  + ¹⁄₁₂

(2A + 2B + 2C)'s 1 day work = ⅙ + ⅛  + ¹⁄₁₂

2  ⋅  (A + B + C)'s 1 day work =  ⅙ + ⅛  + ¹⁄₁₂

L.C.M of (6, 8, 12) = 24.

2 (A + B + C)'s 1 day work = ⁴⁄₂₄ + ³⁄₂₄ + ²⁄₂₄

2 (A + B + C)'s 1 day work = ⁹⁄₂₄

2 (A + B + C)'s 1 day work = ⅜

(A + B + C)'s 1 day work = ³⁄₁₆

Time taken by A, B and C together to complete the work is

= 5 ⅓  days

Problem 3 :

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

(A + B)'s 1 day work = ¹⁄₁₅

(B + C)'s 1 day work = ¹⁄₃₀

(A + C)'s 1 day work = ¹⁄₁₈

(A + B + B + C + A + C)'s 1 day work = ¹⁄₁₅  +  ¹⁄₃₀ +  ¹⁄₁₈

(2A + 2B + 2C)'s 1 day work = ¹⁄₁₅  +  ¹⁄₃₀ +  ¹⁄₁₈

2 (A + B + C)'s 1 day work =  ¹⁄₁₅  +  ¹⁄₃₀ +  ¹⁄₁₈

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

2 (A + B + C)'s 1 day work = ⁶⁄₉₀ + ³⁄₉₀ + ⁵⁄₉₀

2 (A + B + C)'s 1 day work = ¹⁴⁄₉₀

2 (A + B + C)'s 1 day work = ⁷⁄₄₅

(A + B + C)'s 1 day work = ⁷⁄₉₀

Then, the amount of work completed by A, B and C together in 9 days is

= 9  ⋅  ⁷⁄₉₀

=  ⁷⁄₁₀

Amount of work left for B and C to complete is

=  ³⁄₁₀

Number of days that B will take to finish the work is

= amount of work/part of the work done in 1 day

= ³⁄₁₀   ÷  ¹⁄₃₀

= ³⁄₁₀   ⋅   ³⁰⁄₁

Problem 4 :

A contractor decided to complete the work in 90 days and employed 50 men at the beginning and 20 men additionally after 20 days and got the work completed as per schedule. If he had not employed the additional men, how many extra days would he have needed to complete the work?

The work has to completed in 90 days (as per schedule).

Total no. of men appointed initially = 50.

Given :  50 men have already worked for 20 days and completed a part of the work.

If the remaining work is done by 70 men (50 + 20  = 70), the work can be completed in 70 days and the total work can be completed in 90 days as per the schedule.

Let 'x' be the no. of days required when the remaining work is done by 50 men.

For the remaining work,

70 men ----> 70 days

50 men -----> x days

The above one is a inverse variation.

Because, when no. of men is decreased, no. of days will be increased.

By inverse variation, we have

70  ⋅ 70 = 50 ⋅ x

So, if the remaining work is done by 50 men, it can be completed in 98 days.

So, extra days needed = 98 - 70 = 28 days.

Problem 5 :

Three taps A, B and C can fill a tank in 10, 15 and 20 hours respectively. If A is open all the time and B and C are open for one hour each alternately, find the time taken to fill the tank.

A's 1 hour work = ⅒

B's 1 hour work = ¹⁄₁₅

C's 1 hour work = ¹⁄₂₀

In the first hour, we have

(A + B)'s work = ⅒  + ¹⁄₁₅

(A + B)'s work = ³⁄₃₀ + ²⁄₃₀

(A + B)'s work = ⁵⁄₃₀

(A + B)'s work = ⅙

In the second hour, we have

(A + C)'s work = ⅒  +  ¹⁄₂₀

(A + C)'s work = ²⁄₂₀ +  ¹⁄₂₀

(A + C)'s work = ³⁄₂₀

Amount of work done in each two hours is

= ¹⁰⁄₆₀ +  ⁹⁄₆₀

Amount of work done :

In the first 2 hours :  ¹⁹⁄₆₀

In the first 4 hours : ¹⁹⁄₆₀  + ¹⁹⁄₆₀  = ³⁸⁄₆₀

In the first 6 hours : ¹⁹⁄₆₀  + ¹⁹⁄₆₀  +  ¹⁹⁄₆₀ = ⁵⁷⁄₆₀

After 6 hours, the remaining work will be

=  ¹⁄₂₀

¹⁄₂₀  is the small amount of work left and A alone can complete this.

Time taken by A to complete this 1/20 part of the work is

= amount of work/part of work done in 1 hour

= ¹⁄₂₀  ÷  ⅒

=  ¹⁄₂₀ ⋅ ¹⁰⁄₁

=  ½ hours

So, A will will take half an hour (or 30 minutes) to complete the remaining work ¹⁄₂₀ .

So, total time taken to complete the work is

= 6 hours + 30  minutes

= 6 ½  hours

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Teens and Video Games Today

85% of u.s. teens say they play video games, and about four-in-ten do so daily. teens see both positive and negative sides of video games – from problem-solving and making friends to harassment and sleep loss, table of contents.

• Who plays video games?
• How often do teens play video games?
• What devices do teens play video games on?
• Social media use among gamers
• Teen views on how much they play video games and efforts to cut back
• Are teens social with others through video games?
• Do teens think video games positively or negatively impact their lives?
• Why do teens play video games?
• Bullying and violence in video games
• Appendix A: Detailed charts
• Acknowledgments
• Methodology

Pew Research Center conducted this analysis to better understand teens’ use of and experiences with video games.

The Center conducted an online survey of 1,453 U.S. teens from Sept. 26 to Oct. 23, 2023, through Ipsos. Ipsos recruited the teens via their parents, who were part of its KnowledgePanel . The KnowledgePanel is a probability-based web panel recruited primarily through national, random sampling of residential addresses. The survey was weighted to be representative of U.S. teens ages 13 to 17 who live with their parents by age, gender, race and ethnicity, household income, and other categories.

This research was reviewed and approved by an external institutional review board (IRB), Advarra, an independent committee of experts specializing in helping to protect the rights of research participants.

Here are the questions used for this analysis , along with responses, and  its methodology .

There are long-standing debates about the impact of video games on youth. Some credit them for helping young people form friendships and teaching them about teamwork and problem-solving . Others say video games expose teenagers to violent content, negatively impact their sleep and can even lead to addiction.

With this in mind, Pew Research Center surveyed 1,423 U.S. teens ages 13 to 17 about their own video game habits – from how often they play to the friends they’ve made and whether it gets in the way of them doing well in school or getting a good night’s sleep. 1

Key findings from the survey

• Video games as a part of daily teen life: 85% of U.S. teens report playing video games, and 41% say they play them at least once a day. Four-in-ten identify as a gamer.
• Gaming as a social experience: 72% of teens who play video games say that a reason why they play them is to spend time with others. And some have even made a friend online from playing them – 47% of teen video game players say they’ve done this.
• Helpful with problem-solving, less so for sleep: Over half of teens who play video games say it has helped their problem-solving skills, but 41% also say it has hurt their sleep.
• Bullying is a problem: 80% of all teens think harassment over video games is a problem for people their age. And 41% of those who play them say they’ve been called an offensive name when playing.
• Boys’ and girls’ experiences differ: Most teen boys and girls play video games, but larger shares of boys identify as gamers (62% vs. 17%) and play every day (61% vs. 22%). Boys who play them are also more likely to experience positive things from it, like making friends, and more troubling things like harassment.

Jump to read about: Who plays video games | Socializing over video games | Views about video games’ impact | Harassment and violence in video games      

Playing video games is widespread among teens. The vast majority of U.S. teens (85%) say they play them. Just 15% say they never do, according to the survey conducted Sept. 26-Oct. 23, 2023.

In addition to asking whether teens play video games, we also wanted to learn whether they consider themselves gamers. Overall, four-in-ten U.S. teens think of themselves as gamers. Just under half of teens (45%) play video games but do not think of themselves as gamers.

Nearly all boys (97%) say they play video games, compared with about three-quarters of teen girls. There is a substantial gap by gender in whether teens identify as gamers: 62% of teen boys do, compared with 17% of girls. 2

By gender and age

Younger teen girls are more likely than older girls to say they play video games: 81% of girls ages 13 to 14 compared with 67% of those ages 15 to 17. But among boys, nearly all play video games regardless of age. 

Similar shares of teens play video games across different racial and ethnic groups and among those who live in households with different annual incomes. Go to Appendix A for more detail on which teens play video games and which teens identify as gamers.

We also asked teens how often they play video games. About four-in-ten U.S. teens say they play video games daily, including 23% who do so several times a day.

Another 22% say they play several times a week, while 21% play them about once a week or less.

Teen boys are far more likely than girls to say they play video games daily (61% vs. 22%). They are also much more likely to say they play them several times a day (36% vs. 11%).

By whether someone identifies as a gamer

About seven-in-ten teens who identify as gamers (71%) say they play video games daily. This drops to 30% among those who play them but aren’t gamers.

By household income

Roughly half of teens living in households with an annual income of less than $30,000 (53%) say they play video games at least daily. This is higher than those in households with an annual income of $30,000 to $74,999 (42%) and $75,000 or more (39%).

Go to Appendix A to see more details about who plays video games and identifies as a gamer by gender, age, race and ethnicity, and household income.

Most teens play video games on a gaming console or a smartphone. When asked about five devices, most teens report playing video games on a gaming console (73%), such as PlayStation, Switch or Xbox. And 70% do so on a smartphone. Fewer – though still sizable shares – play them on each of the following:

• 49% say they play them on a desktop or laptop computer
• 33% do so on a tablet  
• 24% play them on a virtual reality (VR) headset such as Oculus, Meta Quest or PlayStation VR

Many teens play video games on multiple devices. About a quarter of teens (27%) do so on at least four of the five devices asked about, and about half (49%) play on two or three of them. Just 8% play video games on one device.

Teen boys are more likely than girls to play video games on four of the five devices asked about – all expect tablets. For instance, roughly nine-in-ten teen boys say they ever play video games on a gaming console, compared with 57% of girls. Equal shares of teen boys and girls play them on tablets.  

Teens who consider themselves gamers are more likely than those who play video games but aren’t gamers to play on a gaming console (95% vs. 78%), desktop or laptop computer (72% vs. 45%) or a virtual reality (VR) headset (39% vs. 19%). Similar shares of both groups play them on smartphones and tablets.

One way that teens engage with others about video games is through online platforms. And our survey findings show that teen gamers stand out for their use of two online platforms that are known for their gaming communities – Discord and Twitch :

• 44% of teen gamers say they use Discord, far higher than video game players who don’t identify as gamers or those who use the platform but do not play video games at all. About three-in-ten teens overall (28%) use Discord.
• 30% of teens gamers say they use Twitch. About one-in-ten other teens or fewer say the same; 17% of teens overall use the platform.

Previous Center research shows that U.S. teens use online platforms at high rates .

Teens largely say they spend the right amount of time playing video games. When asked about how much time they spend playing them, the largest share of teens (58%) say they spend the right amount of time. Far fewer feel they spend too much (14%) or too little (13%) time playing them.

Teen boys are more likely than girls to say they spend too much time playing video games (22% vs. 6%).

By race and ethnicity

Black (17%) and Hispanic (18%) teens are about twice as likely than White teens (8%) to say they spend too little time playing video games. 3

A quarter of teens who consider themselves gamers say they spend too much time playing video games, compared with 9% of those who play video games but don’t identify as gamers. Teen gamers are also less likely to think they spend too little time playing them (19% vs. 10%).

Fewer than half of teens have reduced how much they play video games. About four-in-ten (38%) say they have ever chosen to cut back on the amount of time they spend playing them. A majority (61%) report that they have not cut back at all.

This share is on par with findings about whether teenagers have cut back with their screen time – on social media or their smartphone.

Although boys are more likely to say they play video games too much, boys and girls are on par for whether they have ever cut back. About four-in-ten teen boys (39%) and girls (38%) say that they have ever cut back.

And gamers are as likely to say they have cut back as those who play video games but don’t identify as gamers (39% and 41%).

A main goal of our survey was to ask teens about their own experiences playing video games. For this section of the report, we focus on teens who say they play video games.

Socializing with others is a key part of the video game experience. Most teens who play video games do so with others, and some have developed friendships through them.

About nine-in-ten teen video game players (89%) say they play them with other people, in person or online. Far fewer (11%) play them only on their own.

Additionally, about half (47%) report that they have ever made a friend online because of a video game they both play. This equals 40% of all U.S. teens who have made a friend online because of a video game.

These experiences vary by:  

• Gender: Most teen boy and girl video game players play them with others, though it’s more common among boys (94% vs. 82%). Boys who play video games are much more likely to say they have made a friend online because of a video game (56% vs. 35%).
• Race and ethnicity: Black (55%) and Hispanic (53%) teen video game players are more likely than White teen video game players (43%) to say they have made a friend online because of them.
• Whether someone identifies as a gamer: Nearly all teen gamers report playing video games with others (98%). Fewer – though still most – of those who play video games but aren’t gamers (81%) also play them with others. And about seven-in-ten (68%) say they have made a friend online because of a video game, compared with 29% of those who play them but don’t identify as gamers.

Teens who play video games are particularly likely to say video games help their problem-solving skills. More than half of teens who play video games (56%) say this.

Additionally, more think that video games help, rather than hurt, three other parts of their lives that the survey asked about. Among teens who play video games:

• Roughly half (47%) say it has helped their friendships
• 41% say it has helped how they work with others
• 32% say it has helped their mental health

No more than 7% say playing video games has hurt any of these.

More teens who play video games say it hurts, rather than helps, their sleep. Among these teens, 41% say it has hurt how much sleep they get, while just 5% say it helps. And small shares say playing video games has impacted how well they do in school in either a positive or a negative way.

Still, many teens who play video games think playing them doesn’t have much an impact in any of these areas. For instance, at least six-in-ten teens who play video games say it has neither a positive nor a negative impact on their mental health (60%) or their school performance (72%). Fewer (41%) say this of their problem-solving skills.

Teen boys who play video games are more likely than girls to think playing them has helped their problem-solving skills, friendships and ability to work with others. For instance, 55% of teen boys who play video games say this has helped their friendships, compared with 35% of teen girls.

As for ways that it may hurt their lives, boys who play them are more likely than girls to say that it has hurt the amount of sleep they get (45% vs. 37%) and how well they do in school (21% vs. 11%). 

Teens who consider themselves gamers are more likely than those who aren’t gamers but play video games to say video games have helped their friendships (60% vs. 35%), ability to work with others (52% vs. 32%), problem-solving skills (66% vs. 47%) and mental health (41% vs. 24%).

Gamers, though, are somewhat more likely to say playing them hurt their sleep (48% vs. 36%) and how well they do in school (20% vs. 14%).

By whether teens play too much, too little or the right amount

Teens who report playing video games too much stand out for thinking video games have hurt their sleep and school performance. Two-thirds of these teens say it has hurt the amount of sleep they get, and 39% say it hurt their schoolwork. Far fewer of those who say they play the right amount (38%) or too little (32%) say it has hurt their sleep, or say it hurt their schoolwork (12% and 16%).

Teens who play video games say they largely do so to be entertained. And many also play them to be social with and interact with others. Teens who play video games were asked about four reasons why they play video games. Among those who play video games:

• Nearly all say fun or entertainment is a major or minor reason why they play video games – with a large majority (87%) saying it’s a major reason.
• Roughly three-quarters say spending time with others is a reason, and two-thirds say this of competing with others. Roughly three-in-ten say each is a major reason.
• Fewer – 50% – see learning something as a reason, with just 13% saying it’s a major reason.

While entertainment is by far the most common reason given by teens who play video games, differences emerge across groups in why they play video games.

Teens who identify as gamers are particularly likely to say each is major reason, especially when it comes to competing against others. About four-in-ten gamers (43%) say this is a major reason, compared with 13% of those who play video games but aren’t gamers.

Teen boys who play video games are more likely than girls to say competing (36% vs. 15%), spending time with others (36% vs. 27%) and entertainment (90% vs. 83%) are major reasons they play video games.

Black and Hispanic teens who play video games are more likely than White teens to say that learning new things and competing against others are major reasons they play them. For instance, 29% of Black teen video game players say learning something new is a major reason, higher than 17% of Hispanic teen video game players. Both are higher than the 7% of White teen video game players who say the same.

Teens who play video games and live in lower-income households are especially likely to say competing against others and learning new things are major reasons. For instance, four-in-ten teen video game players who live in households with an annual income of less than $30,000 say competing against others is a major reason they play. This is higher than among those in households with annual incomes of $30,000 to $74,999 (29%) and $75,000 or more (23%).

Cyberbullying can happen in many online environments, but many teens encounter this in the video game world.

Our survey finds that name-calling is a relatively common feature of video game life – especially for boys. Roughly four-in-ten teen video game players (43%) say they have been harassed or bullied while playing a video game in one of three ways: 

• 41% have been called an offensive name
• 12% have been physically threatened
• 8% have been sent unwanted sexually explicit things

Teen boys are particularly likely to say they have been called an offensive name. About half of teen boys who play video games (48%) say this has happened while playing them, compared with about a third of girls (32%). And they are somewhat more likely than girls to have been physically threatened (15% vs. 9%).

Teen gamers are more likely than those who play video games but aren’t gamers to say they been called and offensive name (53% vs. 30%), been physically threatened (17% vs. 8%) and sent unwanted sexually explicit things (10% vs. 6%).

Teens – regardless of whether they’ve had these experiences – think bullying is a problem in gaming. Eight-in-ten U.S. teens say that when it comes to video games, harassment and bullying is a problem for people their age. This includes 29% who say it is a major problem.

It’s common for teens to think harassment while playing video games is a problem, but girls are somewhat more likely than boys to say it’s a major problem (33% vs. 25%).

There have also been decades-long debates about how violent video games can influence youth behavior , if at all – such as by encouraging or desensitizing them to violence. We wanted to get a sense of how commonly violence shows up in the video games teens are playing.

Just over half of teens who play video games (56%) say at least some of the games they play contain violence. This includes 16% who say it’s in all or most of the games they play.

Teen boys who play video games are far more likely than girls to say that at least some of the games they play contain violence (69% vs. 37%).

About three-quarters of teen gamers (73%) say that at least some of the games they play contain violence, compared with 40% among video game players who aren’t gamers.   

• Throughout this report, “teens” refers to those ages 13 to 17. ↩
• Previous Center research of U.S. adults shows that men are more likely than women to identify as gamers – especially the youngest adults. ↩
• There were not enough Asian American respondents in the sample to be broken out into a separate analysis. As always, their responses are incorporated into the general population figures throughout the report. ↩

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NATIONAL BIKE MONTH

May is National Bike Month, so here are a few problems related to bicycles.

Brenden is riding an old-time bicycle that has a back wheel with a diameter of 1 foot and a front wheel with a radius of 1.5 feet. After traveling 1000 feet, how many more rotations than the front tire has the back tire completed? Express your answer to the nearest whole number.

Jermaine starts riding his bike at a rate of 10 miles per hour. After 5 minutes, Nelson starts riding from the same starting point as Jermaine and along the same route at a rate of 12 miles per hour. If each boy rides at a constant rate, how many minutes will Jermaine ride his bike for before Nelson catches up with him?

At Your Town Bike Shop, handle bar streamers are sold in packs of two and beads for spokes are sold in sets of 10. Georgina purchases 2 packs of handle bar streamers and 3 sets of beads for $27.85 before tax. Alexis purchases 1 pack of streamers and 4 sets of beads for $26.30 before tax. If Nana wants to buy 3 packs of streamers and 6 sets of beads, how much will her bill be before tax?

CHECK THE PROBLEM OF THE WEEK ARCHIVE FOR SOLUTIONS TO PREVIOUS PROBLEMS

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Hersh: Now is time to be citizens, not spectators

Let’s commit to solutions instead of accepting impasse..

By Ken Hersh

12:00 PM on May 11, 2024 CDT

President George W. Bush implored Americans to be “citizens, not spectators” in his first inaugural address. In that capacity, we have an obligation to get involved. On March 17, The Dallas Morning News published “ A survival guide for a moderate conservative, ” in which I suggested that we all become policy venture capitalists at times of great need.

Now is that time.

We find ourselves living in a divided country, full of well-documented acrimony. At the heart of this division lies a set of issues that are quite fundamental. How will our freedoms be balanced against other national priorities? How will we relate to ever-changing technology? What is the proper role of government in our lives? What will be our role in the world?

These are heady questions that will not be resolved quickly. If the problems were easy, they would have already been solved, and this is not the first time our nation has confronted seemingly intractable choices.

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This election year, we should also remember that these issues are unlikely to be solved during one presidential term. It is critical that we play the long game.

I view our democracy as an investor approaching opportunities. I look for good ideas to solve important problems. I look for resourceful people willing to tackle a cause and who are not afraid to take some risk. I look for adaptable people since change is the only constant in business. Our country is full of such people who are working to solve today’s challenges.

Some of them are scholars in the George W. Bush Institute’s leadership programs. Others are lawmakers. And many more are rising from the grassroots in our own communities. We all need to understand that these foot soldiers of our democracy are vitally important, even if they don’t generate the outrage that gets noted on cable news or social media.

One such problem-solver is Utah Gov. Spencer Cox, chair of the National Governors Association and founder of its Disagree Better initiative. Cox, a Republican, appeared at the Bush Center earlier this year with Kansas Gov. Laura Kelly, a Democrat, and presented some tips : Don’t make false assumptions, find common ground, don’t make blanket statements, take a break from conversations going nowhere and address the ideas rather than the individual.

Another problem-solver, Dallas Fire-Rescue Deputy Chief Steve Lopez, used his network to solve a problem in his own backyard. Lopez, a member of our Presidential Leadership Scholars program, oversees training, professional development and fleet maintenance for Dallas Fire-Rescue. He discovered that a shortage of mechanics was threatening the department’s ability to respond quickly to emergency situations. So he changed the recruiting and training methods, thanks to inspiration from his Presidential Leadership Scholar colleague Mary Martha Henson, who works on workforce development issues in Mississippi.

Two other Presidential Leadership Scholars — Tony Vargas, a Democratic state senator from Nebraska, and Jared Lyon, a CEO of a nonprofit serving student veterans — have a similar story of collaboration. Lyon had been working with universities to better support transitioning veterans. He proposes automatic admission to any active-duty or veteran student who meets admission requirements and is also a resident of the state.

In a conversation one day between the two scholars, Vargas recommended that the idea should be state law and that he wanted to take it on. That was the catalyst for enacted legislation in Nebraska and has become a blueprint for other states.

These are wonderful examples of people from differing perspectives who mobilized their networks to get things done.

This is why I say, “act big in small ways.” Avoid the noise of the complainers and avoid the tendency to federalize your local concerns. Ordinary people can do extraordinary things. None of us are powerless.

Find an issue that you feel most passionate about. Appreciate both sides of the debate and work constructively on solutions. You will be amazed at the progress that’s possible. Even if the solution is not immediate, constructive ideas that are well disseminated find a prominent place on the shelf until the time is right.

If we commit to solutions instead of accepting impasse, we’ll be part of the answer, not part of the problem. And future generations will get a huge return on our investment in this great nation.

Ken Hersh is president and CEO of the George W. Bush Presidential Center and co-founder and former CEO of NGP Energy Capital Management.

Editor’s note: On March 17, The Dallas Morning News published a column by Ken Hersh which gave advice for citizenship habits that can help readers navigate this election year. This column is one in a series that expands on those ideas.

We welcome your thoughts in a letter to the editor. See the guidelines and submit your letter here . If you have problems with the form, you can submit via email at [email protected]

How the state’s complex toll system is choking thousands of Texas drivers

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A Plan to Remake the Middle East

While talks for a cease-fire between israel and hamas continue, another set of negotiations is happening behind the scenes..

This transcript was created using speech recognition software. While it has been reviewed by human transcribers, it may contain errors. Please review the episode audio before quoting from this transcript and email [email protected] with any questions.

From New York Times, I’m Michael Barbaro. This is The Daily.

[MUSIC CONTINUES]

Today, if and when Israel and Hamas reach a deal for a ceasefire fire, the United States will immediately turn to a different set of negotiations over a grand diplomatic bargain that it believes could rebuild Gaza and remake the Middle East. My colleague Michael Crowley has been reporting on that plan and explains why those involved in it believe they have so little time left to get it done.

It’s Wednesday, May 8.

Michael, I want to start with what feels like a pretty dizzying set of developments in this conflict over the past few days. Just walk us through them?

Well, over the weekend, there was an intense round of negotiations in an effort, backed by the United States, to reach a ceasefire in the Gaza war.

The latest ceasefire proposal would reportedly see as many as 33 Israeli hostages released in exchange for potentially hundreds of Palestinian prisoners.

US officials were very eager to get this deal.

Pressure for a ceasefire has been building ahead of a threatened Israeli assault on Rafah.

Because Israel has been threatening a military offensive in the Southern Palestinian city of Rafah, where a huge number of people are crowded.

Fleeing the violence to the North. And now they’re packed into Rafah. Exposed and vulnerable, they need to be protected.

And the US says it would be a humanitarian catastrophe on top of the emergency that’s already underway.

Breaking news this hour — very important breaking news. An official Hamas source has told The BBC that it does accept a proposal for a ceasefire deal in Gaza.

And for a few hours on Monday, it looked like there might have been a major breakthrough when Hamas put out a statement saying that it had accepted a negotiating proposal.

Israeli Prime Minister Benjamin Netanyahu says the ceasefire proposal does not meet his country’s requirements. But Netanyahu says he will send a delegation of mediators to continue those talks. Now, the terms —

But those hopes were dashed pretty quickly when the Israelis took a look at what Hamas was saying and said that it was not a proposal that they had agreed to. It had been modified.

And overnight —

Israeli troops stormed into Rafah. Video showing tanks crashing over a sign at the entrance of the city.

— the Israelis launched a partial invasion of Rafah.

It says Hamas used the area to launch a deadly attack on Israeli troops over the weekend.

And they have now secured a border crossing at the Southern end of Gaza and are conducting targeted strikes. This is not yet the full scale invasion that President Biden has adamantly warned Israel against undertaking, but it is an escalation by Israel.

So while all that drama might suggest that these talks are in big trouble, these talks are very much still alive and ongoing and there is still a possibility of a ceasefire deal.

And the reason that’s so important is not just to stop the fighting in Gaza and relieve the suffering there, but a ceasefire also opens the door to a grand diplomatic bargain, one that involves Israel and its Arab neighbors and the Palestinians, and would have very far-reaching implications.

And what is that grand bargain. Describe what you’re talking about?

Well, it’s incredibly ambitious. It would reshape Israel’s relationship with its Arab neighbors, principally Saudi Arabia. But it’s important to understand that this is a vision that has actually been around since well before October 7. This was a diplomatic project that President Biden had been investing in and negotiating actually in a very real and tangible way long before the Hamas attacks and the Gaza war.

And President Biden was looking to build on something that President Trump had done, which was a series of agreements that the Trump administration struck in which Israel and some of its Arab neighbors agreed to have normal diplomatic relations for the first time.

Right, they’re called the Abraham Accords.

That’s right. And, you know, Biden doesn’t like a lot of things, most things that Trump did. But he actually likes this, because the idea is that they contribute to stability and economic integration in the Middle East, the US likes Israel having friends and likes having a tight-knit alliance against Iran.

President Biden agrees with the Saudis and with the Israelis, that Iran is really the top threat to everybody here. So, how can you build on this? How can you expand it? Well, the next and biggest step would be normalizing relations between Israel and Saudi Arabia.

And the Saudis have made clear that they want to do this and that they’re ready to do this. They weren’t ready to do it in the Trump years. But Mohammed bin Salman, the Crown Prince of Saudi Arabia, has made clear he wants to do it now.

So this kind of triangular deal began to take shape before October 7, in which the US, Israel, and Saudi Arabia would enter this three way agreement in which everyone would get something that they wanted.

And just walk through what each side gets in this pre-October 7th version of these negotiations?

So for Israel, you get normalized ties with its most important Arab neighbor and really the country that sets the tone for the whole Muslim world, which is Saudi Arabia of course. It makes Israel feel safer and more secure. Again, it helps to build this alliance against Iran, which Israel considers its greatest threat, and it comes with benefits like economic ties and travel and tourism. And Prime Minister Benjamin Netanyahu has been very open, at least before October 7th, that this was his highest diplomatic and foreign policy priority.

For the Saudis, the rationale is similar when it comes to Israel. They think that it will bring stability. They like having a more explicitly close ally against Iran. There are economic and cultural benefits. Saudi Arabia is opening itself up in general, encouraging more tourism.

But I think that what’s most important to the Crown Prince, Mohammed bin Salman, is what he can get from the United States. And what he has been asking for are a couple of essential things. One is a security agreement whose details have always been a little bit vague, but I think essentially come down to reliable arms supplies from the United States that are not going to be cut off or paused on a whim, as he felt happened when President Biden stopped arms deliveries in 2021 because of how Saudi was conducting its war in Yemen. The Saudis were furious about that.

Saudi Arabia also wants to start a domestic nuclear power program. They are planning for a very long-term future, possibly a post-oil future. And they need help getting a nuclear program off the ground.

And they want that from the US?

And they want that from the US.

Now, those are big asks from the us. But from the perspective of President Biden, there are some really enticing things about this possible agreement. One is that it will hopefully produce more stability in the region. Again, the US likes having a tight-knit alliance against Iran.

The US also wants to have a strong relationship with Saudi Arabia. You know, despite the anger at Mohammed bin Salman over the murder of the Saudi dissident Jamal Khashoggi, the Biden administration recognizes that given the Saudis control over global oil production and their strategic importance in the Middle East, they need to have a good relationship with them. And the administration has been worried about the influence of China in the region and with the Saudis in particular.

So this is an opportunity for the US to draw the Saudis closer. Whatever our moral qualms might be about bin Salman and the Saudi government, this is an opportunity to bring the Saudis closer, which is something the Biden administration sees as a strategic benefit.

All three of these countries — big, disparate countries that normally don’t see eye-to-eye, this was a win-win-win on a military, economic, and strategic front.

That’s right. But there was one important actor in the region that did not see itself as winning, and that was the Palestinians.

[MUSIC PLAYING]

First, it’s important to understand that the Palestinians have always expected that the Arab countries in the Middle East would insist that Israel recognize a Palestinian state before those countries were willing to essentially make total peace and have normal relations with Israel.

So when the Abraham Accords happened in the Trump administration, the Palestinians felt like they’d been thrown under the bus because the Abraham Accords gave them virtually nothing. But the Palestinians did still hold out hope that Saudi Arabia would be their savior. And for years, Saudi Arabia has said that Israel must give the Palestinians a state if there’s going to be a normal relationship between Israel and Saudi Arabia.

Now the Palestinians see the Saudis in discussions with the US and Israel about a normalization agreement, and there appears to be very little on offer for the Palestinians. And they are feeling like they’re going to be left out in the cold here.

Right. And in the minds of the Palestinians, having already been essentially sold out by all their other Arab neighbors, the prospect that Saudi Arabia, of all countries, the most important Muslim Arab country in the region, would sell them out, had to be extremely painful.

It was a nightmare scenario for them. And in the minds of many analysts and US officials, this was a factor, one of many, in Hamas’s decision to stage the October 7th attacks.

Hamas, like other Palestinian leaders, was seeing the prospect that the Middle East was moving on and essentially, in their view, giving up on the Palestinian cause, and that Israel would be able to have friendly, normal relations with Arab countries around the region, and that it could continue with hardline policies toward the Palestinians and a refusal, as Prime Minister Benjamin Netanyahu has said publicly, to accept a Palestinian state.

Right. So Michael, once Hamas carries out the October 7th attacks in an effort to destroy a status quo that it thinks is leaving them less and less relevant, more and more hopeless, including potentially this prospect that Saudi Arabia is going to normalize relations with Israel, what happens to these pre-October 7th negotiations between the US, Saudi Arabia, and Israel?

Well, I think there was a snap assumption that these talks were dead and buried. That they couldn’t possibly survive a cataclysm like this.

But then something surprising happened. It became clear that all the parties were still determined to pull-off the normalization.

And most surprisingly of all, perhaps, was the continued eagerness of Saudi Arabia, which publicly was professing outrage over the Israeli response to the Hamas attacks, but privately was still very much engaged in these conversations and trying to move them forward.

And in fact, what has happened is that the scope of this effort has grown substantially. October 7th didn’t kill these talks. It actually made them bigger, more complicated, and some people would argue, more important than ever.

We’ll be right back.

Michael, walk us through what exactly happens to these three-way negotiations after October 7th that ends up making them, as you just said, more complicated and more important than ever?

Well, it’s more important than ever because of the incredible need in Gaza. And it’s going to take a deal like this and the approval of Saudi Arabia to unlock the kind of massive reconstruction project required to essentially rebuild Gaza from the rubble. Saudi Arabia and its Arab friends are also going to be instrumental in figuring out how Gaza is governed, and they might even provide troops to help secure it. None of those things are going to happen without a deal like this.

Fascinating.

But this is all much more complicated now because the price for a deal like this has gone up.

And by price, you mean?

What Israel would have to give up. [MUSIC PLAYING]

From Saudi Arabia’s perspective, you have an Arab population that is furious at Israel. It now feels like a really hard time to do a normalization deal with the Israelis. It was never going to be easy, but this is about as bad a time to do it as there has been in a generation at least. And I think that President Biden and the people around him understand that the status quo between Israel and the Palestinians is intolerable and it is going to lead to chaos and violence indefinitely.

So now you have two of the three parties to this agreement, the Saudis and the Americans, basically asking a new price after October 7th, and saying to the Israelis, if we’re going to do this deal, it has to not only do something for the Palestinians, it has to do something really big. You have to commit to the creation of a Palestinian state. Now, I’ll be specific and say that what you hear the Secretary of State, Antony Blinken, say is that the agreement has to include an irreversible time-bound path to a Palestinian state.

We don’t know exactly what that looks like, but it’s some kind of a firm commitment, the likes of which the world and certainly the Israelis have not made before.

Something that was very much not present in the pre-October 7th vision of this negotiation. So much so that, as we just talked about, the Palestinians were left feeling completely out in the cold and furious at it.

That’s right. There was no sign that people were thinking that ambitiously about the Palestinians in this deal before October 7th. And the Palestinians certainly felt like they weren’t going to get much out of it. And that has completely changed now.

So, Michael, once this big new dimension after October 7th, which is the insistence by Saudi Arabia and the US that there be a Palestinian state or a path to a Palestinian state, what is the reaction specifically from Israel, which is, of course, the third major party to this entire conversation?

Well, Israel, or at least its political leadership, hates it. You know, this is just an extremely tough sell in Israel. It would have been a tough sell before October 7th. It’s even harder now.

Prime Minister Benjamin Netanyahu is completely unrepentantly open in saying that there’s not going to be a Palestinian state on his watch. He won’t accept it. He says that it’s a strategic risk to his country. He says that it would, in effect, reward Hamas.

His argument is that terrorism has forced a conversation about statehood onto the table that wasn’t there before October 7th. Sure, it’s always in the background. It’s a perennial issue in global affairs, but it was not something certainly that the US and Israel’s Arab neighbors were actively pushing. Netanyahu also has — you know, he governs with the support of very right-wing members of a political coalition that he has cobbled together. And that coalition is quite likely to fall apart if he does embrace a Palestinian state or a path to a Palestinian state.

Now, he might be able to cobble together some sort of alternative, but it creates a political crisis for him.

And finally, you know, I think in any conversation about Israel, it’s worth bearing in mind something you hear from senior US officials these days, which is that although there is often finger pointing at Netanyahu and a desire to blame Netanyahu as this obstructionist who won’t agree to deals, what they say is Netanyahu is largely reflecting his population and the political establishment of his country, not just the right-wingers in his coalition who are clearly extremist.

But actually the prevailing views of the Israeli public. And the Israeli public and their political leaders across the spectrum right now with few exceptions, are not interested in talking about a Palestinian state when there are still dozens and dozens of Israeli hostages in tunnels beneath Gaza.

So it very much looks like this giant agreement that once seemed doable before October 7th might be more important to everyone involved than ever, given that it’s a plan for rebuilding Gaza and potentially preventing future October 7th’s from happening, but because of this higher price that Israel would have to pay, which is the acceptance of a Palestinian state, it seems from everything you’re saying, that this is more and more out of reach than ever before and hard to imagine happening in the immediate future. So if the people negotiating it are being honest, Michael, are they ready to acknowledge that it doesn’t look like this is going to happen?

Well, not quite yet. As time goes by, they certainly say it’s getting harder and harder, but they’re still trying, and they still think there’s a chance. But both the Saudis and the Biden administration understand that there’s very little time left to do this.

Well, what do you mean there’s very little time left? It would seem like time might benefit this negotiation in that it might give Israel distance from October 7th to think potentially differently about a Palestinian state?

Potentially. But Saudi Arabia wants to get this deal done in the Biden administration because Mohammed bin Salman has concluded this has to be done under a Democratic president.

Because Democrats in Congress are going to be very reluctant to approve a security agreement between the United States and Saudi Arabia.

It’s important to understand that if there is a security agreement, that’s something Congress is going to have to approve. And you’re just not going to get enough Democrats in Congress to support a deal with Saudi Arabia, who a lot of Democrats don’t like to begin with, because they see them as human rights abusers.

But if a Democratic president is asking them to do it, they’re much more likely to go along.

Right. So Saudi Arabia fears that if Biden loses and Trump is president, that those same Democrats would balk at this deal in a way that they wouldn’t if it were being negotiated under President Biden?

Exactly. Now, from President Biden’s perspective, politically, think about a president who’s running for re-election, who is presiding right now over chaos in the Middle East, who doesn’t seem to have good answers for the Israeli-Palestinian question, this is an opportunity for President Biden to deliver what could be at least what he would present as a diplomatic masterstroke that does multiple things at once, including creating a new pathway for Israel and the Palestinians to coexist, to break through the logjam, even as he is also improving Israel’s relations with Saudi Arabia.

So Biden and the Crown Prince hope that they can somehow persuade Bibi Netanyahu that in spite of all the reasons that he thinks this is a terrible idea, that this is a bet worth taking on Israel’s and the region’s long-term security and future?

That’s right. Now, no one has explained very clearly exactly how this is going to work, and it’s probably going to require artful diplomacy, possibly even a scenario where the Israelis would agree to something that maybe means one thing to them and means something else to other people. But Biden officials refuse to say that it’s hopeless and they refuse to essentially take Netanyahu’s preliminary no’s for an answer. And they still see some way that they can thread this incredibly narrow needle.

Michael, I’m curious about a constituency that we haven’t been talking about because they’re not at the table in these discussions that we are talking about here. And that would be Hamas. How does Hamas feel about the prospect of such a deal like this ever taking shape. Do they see it as any kind of a victory and vindication for what they did on October 7th?

So it’s hard to know exactly what Hamas’s leadership is thinking. I think they can feel two things. I think they can feel on the one hand, that they have established themselves as the champions of the Palestinian people who struck a blow against Israel and against a diplomatic process that was potentially going to leave the Palestinians out in the cold.

At the same time, Hamas has no interest in the kind of two-state solution that the US is trying to promote. They think Israel should be destroyed. They think the Palestinian state should cover the entire geography of what is now Israel, and they want to lead a state like that. And that’s not something that the US, Saudi Arabia, or anyone else is going to tolerate.

So what Hamas wants is to fight, to be the leader of the Palestinian people, and to destroy Israel. And they’re not interested in any sort of a peace process or statehood process.

It seems very clear from everything you’ve said here that neither Israel nor Hamas is ready to have the conversation about a grand bargain diplomatic program. And I wonder if that inevitably has any bearing on the ceasefire negotiations that are going on right now between the two of them that are supposed to bring this conflict to some sort of an end, even if it’s just temporary?

Because if, as you said, Michael, a ceasefire opens the door to this larger diplomatic solution, and these two players don’t necessarily want that larger diplomatic solution, doesn’t that inevitably impact their enthusiasm for even reaching a ceasefire?

Well, it certainly doesn’t help. You know, this is such a hellish problem. And of course, you first have the question of whether Israel and Hamas can make a deal on these immediate issues, including the hostages, Palestinian prisoners, and what the Israeli military is going to do, how long a ceasefire might last.

But on top of that, you have these much bigger diplomatic questions that are looming over them. And it’s not clear that either side is ready to turn and face those bigger questions.

So while for the Biden administration and for Saudi Arabia, this is a way out of this crisis, these larger diplomatic solutions, it’s not clear that it’s a conversation that the two parties that are actually at war here are prepared to start having.

Well, Michael, thank you very much. We appreciate it.

On Tuesday afternoon, under intense pressure from the US, delegations from Israel and Hamas arrived in Cairo to resume negotiations over a potential ceasefire. But in a statement, Israel’s Prime Minister Benjamin Netanyahu made clear that even with the talks underway, his government would, quote, “continue to wage war against Hamas.”

Here’s what else you need to know today. In a dramatic day of testimony, Stormy Daniels offered explicit details about an alleged sexual encounter with Donald Trump that ultimately led to the hush money payment at the center of his trial. Daniels testified that Trump answered the door in pajamas, that he told her not to worry that he was married, and that he did not use a condom when they had sex.

That prompted lawyers for Trump to seek a mistrial based on what they called prejudicial testimony. But the judge in the case rejected that request. And,

We’ve seen a ferocious surge of anti-Semitism in America and around the world.

In a speech on Tuesday honoring victims of the Holocaust, President Biden condemned what he said was the alarming rise of anti-Semitism in the United States after the October 7th attacks on Israel. And he expressed worry that too many Americans were already forgetting the horrors of that attack.

The Jewish community, I want you to know I see your fear, your hurt, and your pain. Let me reassure you, as your president, you’re not alone. You belong. You always have and you always will.

Today’s episode was produced by Nina Feldman, Clare Toeniskoetter, and Rikki Novetsky. It was edited by Liz O. Baylen, contains original music by Marion Lozano, Elisheba Ittoop, and Dan Powell, and was engineered by Alyssa Moxley. Our theme music is by Jim Brunberg and Ben Landsverk of Wonderly.

That’s it for The Daily. I’m Michael Barbaro. See you tomorrow.

• May 13, 2024   •   27:46 How Biden Adopted Trump’s Trade War With China
• 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
• May 7, 2024   •   27:43 How Changing Ocean Temperatures Could Upend Life on Earth
• 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

Hosted by Michael Barbaro

Featuring Michael Crowley

Produced by Nina Feldman ,  Clare Toeniskoetter and Rikki Novetsky

Edited by Liz O. Baylen

Original music by Marion Lozano ,  Elisheba Ittoop and Dan Powell

Engineered by Alyssa Moxley

Listen and follow The Daily Apple Podcasts | Spotify | Amazon Music | YouTube

If and when Israel and Hamas reach a deal for a cease-fire, the United States will immediately turn to a different set of negotiations over a grand diplomatic bargain that it believes could rebuild Gaza and remake the Middle East.

Michael Crowley, who covers the State Department and U.S. foreign policy for The Times, explains why those involved in this plan believe they have so little time left to get it done.

On today’s episode

Michael Crowley , a reporter covering the State Department and U.S. foreign policy for The New York Times.

Background reading :

Talks on a cease-fire in the Gaza war are once again at an uncertain stage .

Here’s how the push for a deal between Israel and Saudi Arabia looked before Oct. 7 .

From early in the war, President Biden has said that a lasting resolution requires a “real” Palestinian state .

Here’s what Israeli officials are discussing about postwar Gaza.

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10 the wheel of time characters whose stories are changed most from the books.

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Because Of Wheel Of Time's Season 3 Plan, I'm Worried This Major Character Won't Be In The Show

Grey's anatomy: the kai bartley character explained (& where you've seen the actor), found season 2 premiere window confirms shift in release schedule.

• Prime Video's The Wheel of Time makes significant changes to 10 characters, aiming to adapt the series faithfully. Season 3 continues this.
• Adapting a massive series presents challenges, leading to big decisions on cuts and character/story changes. The show's characters differ from the books.
• Characters like Liandrin, Agelmar, and Abel undergo drastic changes in The Wheel of Time adaptation compared to the original novels.

Prime Video's The Wheel of Time adapts Robert Jordan's 14-volume novel series of the same name, significantly changing the stories of 10 characters along the way. The Wheel of Time has largely been a success for Prime Video, thanks in large part to the rich source material it has to draw on. Accordingly, The Wheel of Time season 3 will look to continue adapting the series as faithfully as possible.

Unfortunately, as The Wheel of Time season 2's ending demonstrates, adapting such a massive series presents a host of difficulties. It's impossible for the show to include every character and every storyline, so big decisions have to be made about cuts and character/story changes that can condense the narrative. With that in mind, The Wheel of Time 's characters are often a bit different from their book counterparts, especially 10 characters whose stories are drastically changed from the novels .

The direction Wheel of Time looks to be taking for season 3 creates concerns that a major ally to the main characters will be left out of the show.

10 Liandrin Guirale — Aes Sedai Of The Red Ajah

Has more redeeming qualities in the wheel of time.

Liandrin, who looks set to be one of the major villains in The Wheel of Time 's future , is one character whose story is drastically changed from the book series. One key difference is the storyline in The Wheel of Time season 2 that sees Liandrin desperately trying to become Nynaeve's personal tutor at the White Tower. In the books, Liandrin sees teaching as below her, and spends most of the one lesson she gives Nynaeve trying to pry information on Rand, Mat, and Perrin from her.

The Wheel of Time seasons 1 and 2 are available to stream on Amazon Prime Video.

The next major departure in Liandrin's story is the son she hides in the White Tower in The Wheel of Time season 2. Nothing remotely like this happens in the book series, and it seems to be part of a larger effort to make Liandrin a more sympathetic character, rather than the purely villainous one she is in The Wheel of Time book series. With that in mind, The Wheel of Time show clearly has different ideas about how to use Liandrin's character , so it's safe to expect more story changes for her character in the future.

9 Agelmar Jagad — Lord Of Fal Dara

Killed in the wheel of time season 1.

Also among the book changes in The Wheel of Time is the premature death of Lord Agelmar Jagad in season 1. Lord Agelmar ends up being killed during the Battle of Tarwin's gap when a trolloc throws a spear through his chest, but this is far from the fate his character meets in the novels. In the books, Lord Agelmar is one of the most respected military commanders on the continent, and he is quickly chosen as one of the leading commanders at Tarmon Gai'don in the final book.

The show depicts him as a prickly man with a distrust of Aes Sedai, but he is the opposite in Jordan's novels.

Agelmar's character is also changed from a personality and attitude perspective. The show depicts him as a prickly man with a distrust of Aes Sedai, but he is the opposite in Jordan's novels. The people of Fal Dara, Agelmar included, have a deep respect for Aes Sedai, and they treat anyone from the White Tower as an honored guest. Between his extremely premature death and the personality differences, Agelmar is one of the most drastically changed characters in The Wheel of Time .

8 Abel Cauthon — Mat's Father

Depicted as a drunk in the wheel of time.

Abel Cauthon is debatably the character that The Wheel of Time changes the most from the book series. In Jordan's novels, Abel is a good man, known for his skill with horses and a quarterstaff. He is one of the most respected members of the Two Rivers community, and he plays a huge role in protecting the village from trollocs in The Shadow Rising , the fourth Wheel of Time book. Mat often remembers his father's wisdom and perceptiveness, calling on it in his times of need.

Mat clearly despises his father in the show, making it difficult to reconcile the character with his book counterpart.

The Abel Cauthon depicted in Prime Video's The Wheel of Time could not be further away from this character. Prime Video's Abel is a cowardly drunk who hides in a shack while his children run for their lives from a host of angry trollocs. Mat clearly despises his father in the show, making it difficult to reconcile the character with his book counterpart. Still, it's possible The Wheel of Time will provide Abel with some sort of redemption and nudge him closer to the man he is in the books.

7 Amalisa Jagad — Lady Of Fal Dara

Sister to lord agelmar jagad.

Amalisa Jagad is a character who plays an extremely minor role in Jordan's novels but was given a much more important part to play in The Wheel of Time . At the end of The Wheel of Time season 1, Lady Amalisa creates a circle with Nynaeve and Egwene, drawing on their power to rain lightning on the trolloc army moving through Tarwin's Gap. Amalisa draws so much of the One Power into her body that it burns her to a crisp, but the trollocs are defeated.

Amalisa has no training, which means she wouldn't know how to form those weaves, even with the requisite power.

In Jordan's novels, Lady Amalisa has little to no talent with channeling, and would be entirely incapable of weaving lightning, even if she were drawing on the power of others. Amalisa has no training, which means she wouldn't know how to form those weaves, even with the requisite power. In the books, Amalisa's only relevant involvement in the story is being Compulsed by Liandrin to find Rand and his friends , so her story is easily one of the most changed from books to show.

6 Anvaere Damodred — Cairhienin Noblewoman

Moiraine damodred's sister.

In Jordan's novel series, Anvaere Damodred is a character who is briefly mentioned during Moiraine's arc, but she never becomes a real character within the story. Moiraine describes her sister as fun-loving with little desire for any real responsibility, citing this as the reason the Throne of Cairhien passed to Galldrian Riatin. In The Wheel of Time show, however, Anvaere is a clever political player with much more ambition than her book character.

This encourages her to marry her son, Barthanes, to the Queen of Cairhien, demonstrating infinitely more ambition than her book counterpart.

The show's Anvaere resents Moiraine for leaving their family behind, and strives to become powerful enough to outdo her sister. This encourages her to marry her son, Barthanes, to the Queen of Cairhien, demonstrating infinitely more ambition than her book counterpart. Of course, Barthanes turns out to be a darkfriend, but the fact remains that Anvaere Damodred is a totally different character in Prime Video's Wheel of Time adaptation .

5 Uno Nomesta — Shienaran Soldier

Killed in the wheel of time season 2.

Uno Nomesta is another character from Jordan's novels who dies prematurely in The Wheel of Time show, making it impossible to follow his book story. Up until Uno's death at the hands of the Seanchan in The Wheel of Time season 2, Uno's story largely followed his book arc, including joining the group hunting for the Horn of Valere. However, Uno lives far beyond the hunt for the Horn in Jordan's books.

Uno notably becomes a Hero of the Horn in The Wheel of Time season 2, marking another departure from the books.

Uno remains a character for the entire Wheel of Time book series , joining the rebel Aes Sedai in Salidar before fighting valiantly at the Last Battle. He also appears sporadically in other characters' stories, showing up when he's least expected. With that in mind, the remainder of Uno's story will have to be skipped in The Wheel of Time , and while his role is not all that important, it's a shame to lose such an intriguing character so early in the story.

4 Logain Ablar — Ghealdanin False Dragon

Cut off from the one power in the wheel of time season 1.

Logain Ablar's story in Prime Video's The Wheel of Time includes several core aspects of his book story, but the rest of his arc is original to the show . His uprising in Ghealdan and subsequent capture by the Red Ajah happens according to the books, but virtually everything else is original to the show. Logain's convoy passing Rand in Tar Valon is similar to another scene from the books, but it happens in Caemlyn in the novels.

Still, the show has a chance to get Logain's arc back on track by Healing his connection to the One Power and integrating the Asha'man.

Other parts of Logain's story in The Wheel of Time , like killing Kerene Nagashi while trying to escape, do not come from the book series. His presence at an asylum in Cairhien is also contrary to book canon, as is Rand's meeting with him there. It seems possible that Logain could end up teaching Rand to channel, which would be another major departure from the books. Still, the show has a chance to get Logain's arc back on track by Healing his connection to the One Power and integrating the Asha'man.

3 Kerene Nagashi — Aes Sedai Of The Green Ajah

Killed by logain in the wheel of time season 1.

Kerene Nagashi is an Aes Sedai of the Green Ajah who is murdered by the Black Ajah years before the main saga in Jordan's Wheel of Time novels. With that in mind, she obviously didn't have any sort of role to play in the main story, so her inclusion in Prime Video's adaptation of the series is totally original. In The Wheel of Time show, Kerene's only purpose seems to be getting killed by Logain, leading to his gentling.

Considering Kerene has been dead for years in the novels, The Wheel of Time 's showrunners likely saw her as an expendable character they could bring in to facilitate Logain's premature gentling.

Considering Kerene has been dead for years in the novels, The Wheel of Time 's showrunners likely saw her as an expendable character they could bring in to facilitate Logain's premature gentling. Regardless, considering she doesn't even appear directly in Jordan's Wheel of Time books, any involvement her character had with the show was always going to contradict book canon .

2 Verin Mathwin — Aes Sedai Of The Brown Ajah

One of the most intelligent aes sedai.

Although Verin's character is similar to her book counterpart in terms of personality and attitude, her story is almost entirely new in The Wheel of Time . Verin enters the show in season 2, being introduced as the sister of Adeleas, which is not the case in the books. She then helps Moiraine get back on her feet before returning to the White Tower to investigate the disappearance of Egwene, Nynaeve, and Elayne.

From there, Verin joins Perrin in his quest to free the Two Rivers from trollocs and abusive White Cloaks.

In the books, Verin first appears in Fal Dara before returning to the White Tower with Egwene and the others. Afterward, she joins the party hunting for the Horn of Valere, following them all the way to Falme. From there, Verin joins Perrin in his quest to free the Two Rivers from trollocs and abusive White Cloaks. While Verin could still join the fight for the Two Rivers in The Wheel of Time season 3, it seems unlikely that her show arc will match up with her book arc any time soon .

1 Elyas Machera — Wolfbrother

Perrin's mentor and friend.

Elyas Machera's character is largely similar to his book counterpart, but his story in Prime Video's Wheel of Time adaptation is significantly different. In the books, Elyas meets Perrin and Egwene when they are lost in the wilderness after escaping Shadar Logoth, helping them find their way to civilization. He does not reappear until he joins Perrin's army in Ghealdan much later in the story.

Still, Elyas is likely to get back on track with his book story and become Perrin's wolfbrother mentor.

In the show, however, Elyas makes his first appearance while Perrin and the Shienarans are hunting for the Horn of Valere, showing up and offering to become their Sniffer. Essentially, nothing that Elyas does in The Wheel of Time season 2 happens in the books , and he is more or less used to take the place of another character, the Sniffer named Hurin. Still, Elyas is likely to get back on track with his book story and become Perrin's wolfbrother mentor.

The Wheel of Time

*Availability in US

Not available

Brandon Sanderson and Robert Jordan's expansive fantasy series is brought to life in The Wheel of Time, a fantasy tv series created for Amazon Prime Video. The series follows a woman named Moiraine, a member of the all-female Aes Sedai group who can utilize a great power. Following an attack on a local village, Moiraine heads there to find a villager that may be the reincarnation of an all-powerful dragon that will either save or destroy the world.

Orioles Eye 3 Trade Targets With 9-Time All-Star ‘Melting Down’: Insider

The Baltimore Orioles have surged to the top of the American League East standings to open the season, racking up as many wins as all but two other teams in MLB.

But there has been one clear roster weakness that would make it hard for the team to compete for a deep playoff run this season: the bullpen.

Anointed closer Craig Kimbrel, a nine-time All-Star and two-time Reliever of the Year Award winner who signed a $13 million deal ahead of the season, has blown three saves so far, tied for the third-most in the big leagues . As a result of his poor start, the team has its eyes on three potential replacements that they could add via trade as the deadline approaches, according to Bob Nightengale of USA Today .

“The Baltimore Orioles privately realize that they are going to have to find a closer for the pennant stretch with Craig Kimbrel melting down,” Nightengale wrote. “They have their eyes on St. Louis Cardinals closer Ryan Helsley, Toronto Blue Jays closer Jordan Romano and Astros reliever Ryan Pressly, if their teams become deadline sellers.”

A Baltimore Orioles Trade for Ryan Helsley Would Add an Elite Closer

Of the players Nightengale identified, Helsley is the only one having a truly elite season thus far.

In his sixth MLB season , the 29-year-old righty has maintained a 1.50 ERA, logging 19 strikeouts in 18 innings, with 11 saves in an MLB-leading 16 games finished. He’s currently on a one-year, $3.8 million deal and will be under club control in 2025 as well.

As a result, he’s likely to be a hot trade commodity at midseason. But the Cardinals do seem like they’d listen to offers as they are likely moving toward a rebuild.

“Oddly enough, the most valuable (and realistic) trade chip the Cardinals may be able to leverage at this year’s trade deadline may not be a starting pitcher or big time veteran bat, but rather, their elite closer in Ryan Helsley,” Josh Jacobs noted for Redbird Rants . “Two playoff runs with a closer like Helsley is worth a lot on the market, and past deadlines have shown us that.”

Trading for Jordan Romano, Ryan Pressly Might Not Solve the Baltimore Orioles’ Problems

The other targets mentioned by Nightengale — Romano and Pressly — have strong resumes but have struggled to open 2024, much like Kimbrel.

The 31-year-old Romano is a two-time All-Star, but has been hit for a 4.15 ERA in just 8.2 innings so far this season after returning from the injured list . He is on a one-year, $7.85 million contract this season. 

And the 35-year-old Pressly is also a two-time All-Star, who has struggled with a 5.65 ERA in 14.1 innings so far this season. He has logged no saves as he’s lost the closer role to Astros’ free agent addition Josh Hader. He is in the second season of a two-year, $30 million contract that has a vesting option for next year.

Depending on how things progress for the rest of the season, the Orioles could opt for a few different changes to its bullpen. But it almost seems like a foregone conclusion that Kimbrel won’t be the preferred closer in a coming playoff run.

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3rd grade (Eureka Math/EngageNY)

Course: 3rd grade (eureka math/engageny)   >   unit 2, telling time (labeled clock).

• Telling time on a clock
• Telling time (unlabeled clock)
• Telling time on a number line
• Telling time to the nearest minute (labeled clock)
• Telling time to the nearest minute (unlabeled clock)
• Tell time to the nearest minute
• Telling time review
• Time differences example
• Time differences (within 60 minutes)
• Telling time with number line
• Tell time on the number line
• Time word problems with number line
• Time word problem: puzzle
• Time word problem: travel time
• Telling time word problems (within the hour)

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