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Time: worked examples and method

Foundation · Grade 1 · Non-calculator

This page sets out the method for time in the order you would use it, then walks through the full lesson explanation. For three complete worked examples with the slips that cost marks, see the Time topic page.

Key facts

The method, step by step

Method: counting on to find a duration

When you see 'how long' between two times, jump to the next full hour, then count hours, then add the leftover minutes.

  1. Start at the earlier time.
  2. Count the minutes up to the next whole hour and write them down.
  3. Count whole hours until you are within an hour of the finish time.
  4. Count the final minutes to reach the finish time.
  5. Add up all the jumps. Convert 60 or more minutes into hours.

Method: adding a duration to a start time

When you see 'starts at … and lasts …', add the hours first, then the minutes, in small jumps.

  1. Add minutes to reach the next whole hour first if that makes it easier.
  2. Add the whole hours.
  3. Add any remaining minutes.
  4. If the minutes go over 60, take away 60 and add 1 to the hours.

How the lesson explains it

60, not 100

A clock minute is one sixtieth of an hour. 1 hour 20 minutes is 80 minutes, because 60 + 20 = 80.

You cannot treat 1:20 as the decimal 1.20 hours.

Minutes past the hour

2:40 means 2 hours and 40 minutes.

Forty minutes is 20 minutes short of the next hour.

A gap on the clock

From 2:50 to 3:20, go to the next hour first: 10 minutes. Then 20 more. The gap is 30 minutes.

Subtracting 320 − 250 = 70 is a decimal trick and it is wrong on a clock.

am and pm

am is midnight to just before noon. pm is noon to just before midnight.

12:00 pm is noon. 12:00 am is midnight.

24-hour times

Add 12 to a pm hour to get the 24-hour hour. 7 pm is 19:00.

Midnight is 00:00. Noon is 12:00. Do not add 12 to noon.

Timetables

A bus every 15 minutes from 9:00 gives 9:15, 9:30, 9:45, then 10:00.

When minutes reach 60, carry an hour.

Sixty minutes, not one hundred

Convert hours to minutes by multiplying by 60. 3 hours is 3 × 60 = 180 minutes. A decimal hour splits the 60, not 100. 0.5 hour is half of 60, which is 30 minutes. 3.5 hours is 3 × 60 + 30 = 210 minutes. Writing 3.5 × 100 = 350 treats the hour as if it had 100 minutes.

Minutes to hours uses division by 60 with a remainder. 95 minutes is 1 hour 35 minutes, because 95 - 60 = 35. Do not write 0.95 hours. 35 minutes is 35/60 of an hour, not 0.35 hour.

Adding minutes can cross an hour. 50 minutes after 10:50 is not 10:100. 50 + 50 = 100 minutes, which is 1 hour and 40 minutes, so the time is 11:40. A neater count: 10 minutes takes you to 11:00, and the other 40 minutes take you to 11:40. Carry the hour as soon as the minutes hit 60.

Method: 1. An hour is 60 minutes, not 100. 2. Multiply the hours by 60, and turn a half hour into 30 minutes. 3. Add those minutes.

12-hour time and 24-hour time

A 12-hour clock repeats the hours, so it needs am or pm. A 24-hour clock runs from 00:00 at midnight through 12:00 at noon to 23:59 just before the next midnight. Morning times keep their hour: 8:15 am is 08:15. Write a leading zero if the question uses four figures.

For pm, add 12 to the hour and keep the minutes. 3:20 pm is 15:20. 7:35 pm is 19:35. 11:05 pm is 23:05. Noon is 12:00, not 24:00. Midnight as a start of the day is 00:00. Adding 12 to noon would call noon 24:00, which is not how a timetable writes the middle of the day.

To read a 24-hour time back, subtract 12 if the hour is 13 or more, and mark it pm. 19:35 is 7:35 pm. Hours from 01 to 11 are am. 12:30 is 12:30 pm. A bus listed at 15:20 is an afternoon bus. It is not 3:20 am and it is not 15:20 pm.

Method: 1. Add 12 to a pm hour from 1 to 11 to get 24-hour time. 2. Noon stays 12:00, and midnight is 00:00. 3. The minutes do not change when you convert the hour.

Duration by counting on

Count up to the next whole hour, add the whole hours, then add the minutes after the last hour. From 2:45 pm to 4:20 pm, first write both in 24-hour time if that helps: 14:45 to 16:20. From 14:45 to 15:00 is 15 minutes. From 15:00 to 16:00 is 60 minutes. From 16:00 to 16:20 is 20 minutes. The total is 15 + 60 + 20 = 95 minutes, which is 1 hour 35 minutes.

Subtracting the clock faces as decimals goes wrong. 420 - 245 = 175 is not a time. Minutes borrow 60, not 100. Counting on avoids that borrow.

A morning journey uses the same count. A train leaves at 08:47 and arrives at 11:15. From 08:47 to 09:00 is 13 minutes, because 60 - 47 = 13. From 09:00 to 11:00 is 2 hours, which is 120 minutes. From 11:00 to 11:15 is 15 minutes. Total 13 + 120 + 15 = 148 minutes, or 2 hours 28 minutes.

Method: 1. Count the minutes up to the next whole hour. 2. Add 60 minutes for each whole hour in between. 3. Add the minutes after the last hour, then total them.

A timetable

A timetable lists times in order, usually in 24-hour form. Suppose the school-gate bus runs at 15:40, 16:05 and 16:30. Maya's lesson ends at 15:52. The 15:40 bus has gone. The next bus is 16:05. The gap from 15:52 to 16:05 is 13 minutes.

The interval is the duration from one time to the next. From 15:40 to 16:05 is 25 minutes, and from 16:05 to 16:30 is 25 minutes. The following bus is 16:55. When the minutes pass 60, the hour increases.

Journey time is the gap between two stops, counted on. A bus from 16:05 to 16:48 takes 43 minutes. Do not subtract the four-digit faces 1648 - 1605.

Method: 1. Read the times in order and pick the next one that has not already gone. 2. Count the gap from the start time to that bus or lesson. 3. Give the answer in minutes or in hours and minutes, as the question asks.

Hours as decimals and fractions

Time uses base sixty, so a decimal number of hours is not the same as hours and minutes. The number 2.25 hours is 2 hours and a quarter of an hour. A quarter of 60 minutes is 15 minutes, so 2.25 hours is 2 hours 15 minutes. Change only the part after the point into minutes: 0.25 × 60 = 15. The whole hours stay as they are.

Fractions work the same way. 13/4 hours is 1 hour and 3/4 × 60 = 45 minutes. To go the other way, divide minutes by 60: 150 minutes is 150 ÷ 60 = 2.5 hours, which is 2 hours 30 minutes. In an exam, write the sum for the conversion, then the unit. A common error is to read 2.25 hours as 2 hours 25 minutes, which is not the same thing.

Method: 1. Keep the whole hours and look at the decimal or fraction part. 2. Multiply that part by 60 to turn it into minutes. 3. To go back, divide the minutes by 60 and add the whole hours. 4. Write both units in the answer.

Tip: Useful pairs: 0.25 h is 15 min, 0.5 h is 30 min, 0.75 h is 45 min, 0.1 h is 6 min.

Adding and multiplying durations

Questions ask for the total length of a series, a set of lessons or a repeated task. One episode lasts 1 hour 28 minutes and there are 5 episodes. Change one episode to minutes, 60 + 28 = 88, and multiply: 5 × 88 = 440 minutes. Then divide by 60 to change back: 440 ÷ 60 = 7 remainder 20, so the total is 7 hours 20 minutes.

Do not multiply the hours and minutes separately and forget to carry. If you do, 5 × 1 hour 28 minutes gives 5 hours 140 minutes, and the 140 minutes must be rewritten as 2 hours 20 minutes. Both methods work, but the minutes-only method has fewer places to slip. The question tells you the form of the answer: "in hours and minutes", "in minutes" or "in hours".

Method: 1. Change each duration to minutes. 2. Add or multiply in minutes. 3. Divide by 60 to find the whole hours; the remainder is the minutes. 4. Write the answer in the form the question asks for.

Will they get there in time

A favourite exam question gives a start time, a few durations and a deadline, then asks "Does she get there in time? You must show all your working." Add the durations one stage at a time, writing the clock time after each stage. A film that starts at 15:20 and lasts 1 hour 50 minutes ends at 17:10. A 25 minute walk after that gives 17:35.

Then compare with the deadline, say a bus at 17:45, and write a sentence that answers the question: "Yes, because 17:35 is before 17:45, which is 10 minutes spare". The mark for the conclusion is separate from the marks for the sums, so do not leave it out. Check by working backwards from the bus time if you have time left.

Method: 1. List each stage with its length in minutes. 2. Add the stages onto the start time, one at a time, using hours first and then minutes. 3. Compare the final time with the deadline. 4. Write a full sentence that says yes or no, and give the reason with the times.

Tip: Count on to the next whole hour first. From 15:20 to 16:00 is 40 minutes, which makes the next steps easier.

Crossing midnight and counting days

A long task can run over several days. If someone sets off at 9:15 pm on Friday and walks for 37 hours, split the hours into whole days and a remainder: 37 = 24 + 13. After 24 hours it is 9:15 pm on Saturday. A further 13 hours takes the clock past midnight. From 9:15 pm to midnight is 2 hours 45 minutes, and the remaining 10 hours 15 minutes puts the finish at 10:15 am on Sunday.

Use the 24-hour clock to check: 21:15 plus 13 hours is 34:15, and subtracting 24 gives 10:15 the next day. The day of the week moves on by one each time the clock passes midnight. Write the day with the time, because the question asks "when". For a timetable, read across the row for the stop you need and down to the correct bus, using a ruler to avoid the wrong column.

Method: 1. Split the hours into complete days of 24 and a remainder. 2. Move the day on by the number of complete days. 3. Add the remainder to the clock time, carrying into a new day if the total passes 24:00. 4. Write the day and the time together, with am or pm if the question uses the 12-hour clock.

Remember

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