Time · applications

Applications: Time

10 question types · Primary 4 · each worked step by step with a figure that follows the steps

PSLE

01

A 24-Hour Time on a Cinema Listing

strategySubtract 12 from the Hours / Count Up Through the Hour

A cinema listing shows that a film starts at 19:35. Mei reaches the cinema at 4.50 p.m. (a) What is 19:35 as a 12-hour time? (b) How long does Mei wait until the film starts?

19:35: the hours are 19 − 12 = 74.50 p.m.19:35?
The hours are more than 12, so subtract 12: 19 − 12 = 7.
The hours in 19:35 are more than 12, so it is a p.m. time. Subtract 12 from the hours: 19 − 12 = 7.
step 1 of 5

Change the 24-hour time to a 12-hour time first, so that both times are written the same way. Then count up from the earlier time to the later time, stopping at each full hour.

  1. The hours in 19:35 are more than 12, so it is a p.m. time. Subtract 12 from the hours: 19 − 12 = 7.
  2. (a) 19:35 is 7.35 p.m.
  3. Count up from 4.50 p.m. to the next hour. From 4.50 p.m. to 5.00 p.m. is 10 min.
  4. From 5.00 p.m. to 7.00 p.m. is 2 h. From 7.00 p.m. to 7.35 p.m. is 35 min.
  5. (b) Mei waits 10 min + 2 h + 35 min = 2 h 45 min. Check: 4.50 p.m. is 16:50, and 2 h 45 min after 16:50 is 19:35.

answer(a) 7.35 p.m.; (b) 2 h 45 min

techniqueThe 24-Hour Clock · Time Durations

examsPSLE

Common pitfalls

  • Writing 19:35 as 9.35 p.m. by dropping the 1. The hours after noon go on from 12, so 12 must be subtracted: 19 − 12 = 7.
  • Subtracting the times like decimals: 7.35 − 4.50 = 2.85. An hour has 60 minutes, not 100, so count up through the hour instead.
02

An Overnight Ferry That Crosses Midnight

strategyStop at Midnight / Add the Part Before and the Part After

An overnight ferry leaves the port at 22:40. It arrives at 06:15 the next morning. (a) How long is it from 22:40 to midnight? (b) How long is the whole journey?

22:4023:0006:1520 min
From 22:40 to the next hour, 23:00, is 20 min.
Count up from 22:40 to the next hour. From 22:40 to 23:00 is 20 min.
step 1 of 4

The journey starts on one day and ends on the next, so cut it at midnight. Find the part before midnight and the part after midnight, then add the two parts.

  1. Count up from 22:40 to the next hour. From 22:40 to 23:00 is 20 min.
  2. From 23:00 to midnight, which is 24:00, is 1 h. (a) From 22:40 to midnight is 1 h 20 min.
  3. Midnight is also 00:00, the start of the next day. From 00:00 to 06:15 is 6 h 15 min.
  4. (b) Add the two parts: 1 h 20 min + 6 h 15 min = 7 h 35 min.

answer(a) 1 h 20 min; (b) 7 h 35 min

techniqueThe 24-Hour Clock · Time Durations

examsPSLE

Common pitfalls

  • Subtracting the smaller time from the larger one, 22:40 − 06:15, which gives 16 h 25 min. That is the time from 06:15 to 22:40 on the same day, not the time through the night.
  • Counting from 22:40 to 23:00 as 60 min. There are 60 minutes in an hour, and 40 of them have passed, so only 20 min are left.
03

A Morning Start and an End Time After Noon

strategyBridge Through 12 Noon / Use the Duration in Two Parts

A class starts a nature walk at 10.40 a.m. The walk lasts 2 h 45 min. (a) How long is it from the start of the walk to 12 noon? (b) At what time does the walk end? Give the time as a 12-hour time and as a 24-hour time.

The walk lasts 2 h 45 min.10.40 a.m.11.00 a.m.12 noon?20 min1 h?
From 10.40 a.m. it is 20 min to 11.00 a.m. and 1 h more to 12 noon.
Count up to 12 noon. From 10.40 a.m. to 11.00 a.m. is 20 min, and from 11.00 a.m. to 12 noon is 1 h.
step 1 of 5

The walk starts in the morning and ends in the afternoon. Use part of the 2 h 45 min to reach 12 noon. The part that is left is the time after noon.

  1. Count up to 12 noon. From 10.40 a.m. to 11.00 a.m. is 20 min, and from 11.00 a.m. to 12 noon is 1 h.
  2. (a) From the start of the walk to 12 noon is 1 h 20 min.
  3. Find the part of the walk that is left: 2 h 45 min − 1 h 20 min = 1 h 25 min.
  4. The walk ends 1 h 25 min after 12 noon. After noon the time is p.m., so the walk ends at 1.25 p.m.
  5. (b) For the 24-hour time, add 12 to the hours: 1 + 12 = 13. The walk ends at 1.25 p.m., which is 13:25.

answer(a) 1 h 20 min; (b) 1.25 p.m., which is 13:25

techniqueam and pm · Time Durations · The 24-Hour Clock

examsPSLE · GCSE Higher

Common pitfalls

  • Adding the times like decimals: 10.40 + 2.45 = 12.85. The 40 min and 45 min make 85 min, which is 1 h 25 min, so another hour must be carried.
  • Writing the answer as 1.25 a.m. The walk passes 12 noon, and every time from noon until midnight is p.m.
04

A Start Time Found by Working Backwards

strategyWork Backwards from the End Time / Take Away the Hours, Then the Minutes

A cake must come out of the oven at 17:20. It bakes for 1 h 45 min. Before that, Mrs Tan needs 25 min to mix the cake. (a) At what time must the cake go into the oven? (b) At what time must Mrs Tan start mixing? Give this time as a 12-hour time too.

Go backwards from 17:20.??16:2017:201 hmixing 25 minbaking 1 h 45 min
One hour before 17:20 is 16:20.
Go back 1 h from 17:20. That is 16:20.
step 1 of 5

The end time is known, so go backwards along the timeline. Take away the hours first. Then take away the minutes, stopping at the full hour on the way.

  1. Go back 1 h from 17:20. That is 16:20.
  2. Go back 45 min from 16:20. Going back 20 min reaches 16:00. Going back the other 25 min reaches 15:35.
  3. (a) The cake must go into the oven at 15:35.
  4. Go back 25 min from 15:35 for the mixing: 35 − 25 = 10, so the time is 15:10.
  5. (b) Mrs Tan must start mixing at 15:10. Subtract 12 from the hours: 15 − 12 = 3, so that is 3.10 p.m. Check: 15:10 and 25 min is 15:35, and 1 h 45 min after 15:35 is 17:20.

answer(a) 15:35; (b) 15:10, which is 3.10 p.m.

techniqueThe 24-Hour Clock · Time Durations

examsPSLE

Common pitfalls

  • Adding the baking time to 17:20 and getting 19:05. The cake is finished at 17:20, so the start is earlier and the baking time must be taken away.
  • Taking 45 from 20 the wrong way round and writing 16:25. There are not enough minutes in 16:20, so go back 20 min to 16:00 first and then 25 min more.
05

Three Rides with a Wait Before Each One

strategyTimeline / Add Each Part in Order, Then Add Only the Waits

Ravi joins the queue for his first ride at 13:15. He waits 20 min and the ride lasts 15 min. He waits 40 min for the second ride, which lasts 10 min. He waits 25 min for the third ride, which lasts 20 min. (a) At what time does the third ride end? (b) How long does Ravi wait altogether?

waitride(minutes)20154010252013:1513:3513:50
The first wait ends at 13:35 and the first ride ends at 13:50.
Add the first wait and the first ride. 20 min after 13:15 is 13:35, and 15 min after that is 13:50.
step 1 of 5

Draw the afternoon as a timeline with one block for each wait and one block for each ride. Move along the timeline one block at a time and write the clock time at the end of each block.

  1. Add the first wait and the first ride. 20 min after 13:15 is 13:35, and 15 min after that is 13:50.
  2. Add the second wait of 40 min. The first 10 min reaches 14:00 and the other 30 min reaches 14:30. The ride of 10 min ends at 14:40.
  3. Add the third wait of 25 min. The first 20 min reaches 15:00 and the other 5 min reaches 15:05. The ride of 20 min ends at 15:25.
  4. (a) The third ride ends at 15:25, which is 3.25 p.m.
  5. (b) Add only the waits: 20 + 40 + 25 = 85 min, which is 1 h 25 min. Check: the rides take 15 + 10 + 20 = 45 min, and 85 + 45 = 130 min is 2 h 10 min, the time from 13:15 to 15:25.

answer(a) 15:25, which is 3.25 p.m.; (b) 85 min, which is 1 h 25 min

techniqueThe 24-Hour Clock · Time Durations · Hours and Minutes

examsPSLE

Common pitfalls

  • Giving 2 h 10 min as the waiting time. That is the whole time from 13:15 to 15:25, and it includes the 45 min that Ravi spends on the rides.
  • Writing 13:50 and 40 min as 13:90. Minutes stop at 59, so 10 min of the wait reaches 14:00 and the other 30 min reaches 14:30.
06

A Parking Charge for Each Hour or Part of an Hour

strategyFind the Duration First / A Part of an Hour Is Charged as a Whole Hour

A car park charges $3 for the first hour and $2 for each hour or part of an hour after that. A car enters at 09:50 and leaves at 13:20. (a) How long is the car in the car park? (b) What is the parking charge?

09:5010:0013:0013:2010 min3 h20 min
From 09:50 it is 10 min to 10:00, then 3 h to 13:00, then 20 min to 13:20.
Count up from 09:50. From 09:50 to 10:00 is 10 min, from 10:00 to 13:00 is 3 h, and from 13:00 to 13:20 is 20 min.
step 1 of 5

Find how long the car is parked by counting up through the hours. Then cut that time into hours. A part of an hour at the end is charged as one more whole hour.

  1. Count up from 09:50. From 09:50 to 10:00 is 10 min, from 10:00 to 13:00 is 3 h, and from 13:00 to 13:20 is 20 min.
  2. (a) The car is parked for 10 min + 3 h + 20 min = 3 h 30 min.
  3. The first hour costs $3. That leaves 3 h 30 min − 1 h = 2 h 30 min.
  4. The 2 h 30 min is 2 whole hours and a part of an hour, so it is charged as 3 hours: 3 × $2 = $6.
  5. (b) The parking charge is $3 + $6 = $9.

answer(a) 3 h 30 min; (b) $9

techniqueThe 24-Hour Clock · Time Durations

examsPSLE

Common pitfalls

  • Charging the last 30 min as half an hour, or not charging it. The sign says each hour or part of an hour, so the 30 min costs the same $2 as a whole hour.
  • Charging $2 for the first hour as well. The first hour has its own price of $3, and only the hours after it cost $2 each.
07

A Clock That Is 10 Minutes Fast

strategyA Fast Clock Shows a Later Time / Go Back to Find the Real Time

The clock in Sam's hall is 10 minutes fast. It shows 08:05. Sam's school bus leaves at 08:30 by the real time. (a) What is the real time now? (b) How many minutes does Sam have before the bus leaves?

The clock shows 08:05. It is 10 min fast.07:5508:0008:055 min5 min
Go back 10 min from 08:05: 5 min reaches 08:00 and 5 min more reaches 07:55.
The hall clock is 10 min ahead, so go back 10 min from 08:05. Going back 5 min reaches 08:00. Going back the other 5 min reaches 07:55.
step 1 of 4

A clock that is fast is ahead of the real time. Go back 10 min from the time on the clock to find the real time. Then count up from the real time to the time the bus leaves.

  1. The hall clock is 10 min ahead, so go back 10 min from 08:05. Going back 5 min reaches 08:00. Going back the other 5 min reaches 07:55.
  2. (a) The real time now is 07:55.
  3. Count up from 07:55 to 08:30. From 07:55 to 08:00 is 5 min, and from 08:00 to 08:30 is 30 min.
  4. (b) Sam has 5 + 30 = 35 min before the bus leaves. Check: when the bus leaves, the hall clock shows 08:40, and from 08:05 to 08:40 is also 35 min.

answer(a) 07:55; (b) 35 min

techniqueThe 24-Hour Clock · Time Durations

examsPSLE

Common pitfalls

  • Adding the 10 min and giving 08:15 as the real time. A fast clock already shows a later time than the real one, so the real time is earlier.
  • Counting from 08:05 to 08:30 and answering 25 min. The time 08:05 comes from the fast clock and 08:30 is a real time, so both times must be real times before they are compared.
08

Sunrise, Sunset and the Length of the Night

strategyCount Up from Sunrise to Sunset / The Night Is the Rest of 24 Hours

One day the sun rises at 06:55 and sets at 19:10. (a) How long is it from sunrise to sunset? (b) A whole day has 24 hours. How long is the rest of the day, when the sun is down?

nightdaynight5 min + 12 h + 10 min00:0006:5519:1024:00
From 06:55 it is 5 min to 07:00, then 12 h to 19:00, then 10 min to 19:10.
Count up from 06:55. From 06:55 to 07:00 is 5 min, from 07:00 to 19:00 is 12 h, and from 19:00 to 19:10 is 10 min.
step 1 of 5

Count up from sunrise to sunset, stopping at the full hours. The day and the night make 24 hours together, so the night is what is left when the daytime is taken away from 24 hours.

  1. Count up from 06:55. From 06:55 to 07:00 is 5 min, from 07:00 to 19:00 is 12 h, and from 19:00 to 19:10 is 10 min.
  2. (a) From sunrise to sunset is 5 min + 12 h + 10 min = 12 h 15 min.
  3. Take the daytime away from 24 h. First take away the hours: 24 h − 12 h = 12 h.
  4. Then take away the 15 min. Change one hour to 60 min: 12 h is 11 h 60 min, and 60 − 15 = 45.
  5. (b) The sun is down for 11 h 45 min. Check: 12 h 15 min + 11 h 45 min = 23 h 60 min = 24 h.

answer(a) 12 h 15 min; (b) 11 h 45 min

techniqueThe 24-Hour Clock · Time Durations · Hours and Minutes

examsPSLE

Common pitfalls

  • Writing 24 h − 12 h 15 min = 12 h 15 min, or 12 h 85 min. The 15 min has to come out of one of the hours, so 12 h becomes 11 h 60 min first.
  • Subtracting only the hours, 19 − 6 = 13, and answering more than 13 h. From 06:55 to 19:55 is exactly 13 h, and 19:10 is earlier than 19:55, so the daytime is less than 13 h.
09

The Same Moment in Two Cities

strategyBehind Means Earlier, Ahead Means Later / Pass Midnight and Change the Day

The time in Dubai is 4 hours behind the time in Singapore. (a) Lina in Singapore calls her aunt in Dubai at 3.30 p.m. What is the time in Dubai? (b) Her aunt calls back at 21:45 on Friday, by the time in Dubai. What are the time and the day in Singapore?

Dubai is 4 h behind: go back 4 h.11.30 a.m.12 noon3.30 p.m.3 h 30 min30 min
Going back 3 h 30 min from 3.30 p.m. reaches 12 noon. The other 30 min reaches 11.30 a.m.
Go back 4 h from 3.30 p.m. Going back 3 h 30 min reaches 12 noon. Going back the other 30 min reaches 11.30 a.m.
step 1 of 5

Dubai is behind, so its clocks show an earlier time than Singapore's: go back 4 h. Singapore is ahead of Dubai, so go forward 4 h. When the count passes noon, a.m. and p.m. change. When it passes midnight, the day changes.

  1. Go back 4 h from 3.30 p.m. Going back 3 h 30 min reaches 12 noon. Going back the other 30 min reaches 11.30 a.m.
  2. (a) The time in Dubai is 11.30 a.m.
  3. Singapore is 4 h ahead of Dubai, so go forward 4 h from 21:45 on Friday. The first 2 h 15 min reaches midnight, and Saturday begins.
  4. The part that is left is 4 h − 2 h 15 min = 1 h 45 min. That is 01:45 on Saturday.
  5. (b) In Singapore it is 01:45 on Saturday.

answer(a) 11.30 a.m.; (b) 01:45 on Saturday

techniqueam and pm · The 24-Hour Clock

examsPSLE

Common pitfalls

  • Going forward 4 h in part (a) and answering 7.30 p.m. Dubai is behind Singapore, so the time there is earlier, not later.
  • Writing 25:45 on Friday in part (b). The hours stop at 23. After midnight the clock starts again at 00:00 and the day becomes Saturday.
10

A Week of Practices from One Day's Start and End

strategyFind One Day First / Multiply, Then Change Minutes to Hours and Minutes

Jia Hui has swimming practice from 17:45 to 18:35 on each of 5 days in a week. (a) How long is one practice? (b) How long does she practice in the week? Give the answer in hours and minutes.

17:4518:0018:3515 min35 min
From 17:45 to 18:00 is 15 min, and from 18:00 to 18:35 is 35 min.
Count up from 17:45 to 18:35. From 17:45 to 18:00 is 15 min, and from 18:00 to 18:35 is 35 min.
step 1 of 5

Find how long one practice is by counting up through 18:00. Multiply by the number of days to get the minutes in the week. Then take out groups of 60 min, because each group is one hour.

  1. Count up from 17:45 to 18:35. From 17:45 to 18:00 is 15 min, and from 18:00 to 18:35 is 35 min.
  2. (a) One practice is 15 + 35 = 50 min.
  3. There are 5 practices in the week: 5 × 50 = 250 min.
  4. Change the minutes to hours. 4 × 60 = 240, so 250 min is 4 h and 250 − 240 = 10 min.
  5. (b) She practices for 4 h 10 min in the week.

answer(a) 50 min; (b) 4 h 10 min, which is 250 min

techniqueThe 24-Hour Clock · Hours and Minutes · Time Durations

examsPSLE

Common pitfalls

  • Subtracting like decimals: 18.35 − 17.45 = 0.90, and answering 90 min. From 17:45 it is only 15 min to 18:00, so one practice is 15 + 35 = 50 min.
  • Writing 250 min as 2 h 50 min. One hour is 60 min, not 100 min, so 250 min is 4 groups of 60 min and 10 min more.
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