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Time

Time

Time calculations

Add And Subtract Core + Extended 9 min read

On this page
  1. In this note
  2. Formula bank
  3. 12-hour and 24-hour clocks
  4. Adding and subtracting times
  5. Decimal hours and minutes
  6. Times as fractions, and ages
  7. Ways they test it
  8. Mistakes to avoid
  9. Summary
  10. Practice
  11. Can I do this?
  12. Quiz

In this note

Syllabus 1.15 (0580) / 1.6 practical situations (4024): time
  • 1.15Use the 12-hour and 24-hour clock.
  • 1.15Add and subtract times, including across midnight, and find durations.
  • 1.15Convert between hours and minutes, including decimal hours (2.35 h = 2 h 21 min).

Next: timetables and time zones. Speed, distance and time is in the chapter Kinematics.

Formula bank

UnitsLearn it60 s = 1 min, 60 min = 1 h, 24 h = 1 dayUse it when any time question.
12-hour → 24-hourLearn itpm: add 12 to the hour; 12.xx am → 00 xxUse it when am / pm times.
Decimal hours → minutesLearn itdecimal part \(\times60\)2.35 h = 2 h 21 min.Use it when a decimal number of hours.
Minutes → decimal hoursLearn itminutes \(\div60\)3 h 24 min = 3.4 h.Use it when before a speed calculation.

12-hour and 24-hour clocks

12-hour24-hourNote
12.05 am00 05just after midnight
7.30 am07 30add a leading 0
12.00 noon12 00
2.15 pm14 15pm: add 12 to the hour
11.40 pm23 40
Times are NOT decimals. 14 15 + 50 minutes is 15 05, not 14 65; and 1 h 30 min is NOT 1.30 h (it is 1.5 h).

Try it yourself

1
4.15 pm in 24-hour time?
Show answer

Answer 16 15

2
00 40 in 12-hour time?
Show answer

Answer 12.40 am

Adding and subtracting times

An hour has 60 minutes, not 100, so column arithmetic gives nonsense. Count on in jumps instead: to the next whole hour, then whole hours, then the leftover minutes.

General methodHow to add a duration to a time (and find an end time)

  1. Add the whole hours first.
  2. Then add the minutes: jump to the next whole hour, then the rest.
  3. Past 24 00? Start again from 00 00 - it is the next day.

Example A film starts at 21 50 and lasts 2 h 35 min. When does it end?

Hours first, then minutes through midnight.

  1. 21 50 + 2 h = 23 50
  2. + 10 min = 00 00
  3. + 25 min = 00 25

Answer 00 25 the next day

General methodHow to find how long something takes (a duration)

  1. Convert both times to the 24-hour clock.
  2. Count on from the start to the next whole hour.
  3. Count whole hours to the hour of the finish (through midnight if needed).
  4. Count the last minutes. Add the jumps.

Example A trip starts at 22 25 and finishes at 07 10. How long is it?

Jump to 23 00, then to 07 00, then to 07 10.

  1. 22 25 → 23 00: 35 min
  2. 23 00 → 07 00: 8 h
  3. 07 00 → 07 10: 10 min

Answer 8 h 45 min

General methodHow to find a start time (work backwards)

  1. Subtract the whole hours.
  2. Then subtract the minutes, jumping back to a whole hour first.

Example A film ends at 00 20 and lasted 2 h 35 min. When did it start?

Back 2 hours, then back 35 minutes.

  1. 00 20 − 2 h = 22 20
  2. 22 20 − 35 min = 21 45

Answer 21 45

Try it yourself

1
19 50 + 2 h 42 min?
Show answer

Answer 22 32

2
How long from 08 55 to 13 20?
Show answer

Answer 4 h 25 min

3
A run ends at 09 05 after 2 h 15 min. When did it start?
Show answer

Answer 06 50

Decimal hours and minutes

General methodHow to change between decimal hours and minutes

  1. Decimal hours → minutes: keep the whole hours; decimal part \(\times60\) = minutes.
  2. Hours and minutes → decimal hours: minutes \(\div60\), add to the hours.
Decimal hoursHours and minutesMinutes
0.2515 min15
0.530 min30
2.752 h 45 min165
3.43 h 24 min204
1.11 h 6 min66

Example Change 2.35 hours into hours and minutes.

Multiply the 0.35 by 60.

  1. \(0.35\times60=21\)

Answer 2 h 21 min

Try it yourself

1
1.3 hours in minutes?
Show answer

Answer 78

2
3 h 24 min in hours, as a decimal?
Show answer

Answer 3.4

Times as fractions, and ages

General methodHow to write one time as a fraction of another

  1. Change both into the SAME unit (usually minutes).
  2. Write as a fraction and simplify.

Example Write 54 minutes as a fraction of 2 hours 6 minutes.

2 h 6 min = 126 min.

  1. \(\tfrac{54}{126}\)

Answer \(\tfrac37\)

Ages work like times with 12 months to a year: 14 years 3 months + 28 months = 14 y 3 m + 2 y 4 m = 16 years 7 months.

Ways they test it

Type 1 End time across midnight

"A coach leaves at 23 15; the journey takes 3 h 50 min. Find the arrival time." (1 mark)

Spot it start + duration.

  1. Hours, then minutes, count on.

For example 23 15 + 3 h 50

  1. 23 15 + 3 h = 02 15
  2. + 50 min = 03 05

Answer 03 05

Type 2 Duration

"How long is the journey from 21 50 to 06 35?" (1 mark)

Spot it two times, "how long".

  1. Count on in jumps.

Type 3 Decimal hours

"Change 2.35 hours into hours and minutes." (1 mark)

Spot it a decimal of hours.

  1. Decimal part × 60.

Type 4 Inside a speed question

"Leaves 13 45, arrives 17 09, 289 km. Find the average speed."

Spot it speed with clock times.

  1. Duration, then decimal hours.
  2. Distance ÷ time.

For example 13 45 → 17 09

  1. 3 h 24 min = 3.4 h
  2. 289 ÷ 3.4

Answer 85 km/h

Mistakes to avoid

  • ✗ 14 15 + 50 min = 14 65✓ 15 0560 minutes in an hour.
  • ✗ 2.35 h = 2 h 35 min✓ 2 h 21 minMultiply the decimal by 60.
  • ✗ 23 40 → 06 50 by subtracting✓ count on: 7 h 10 minSubtracting across midnight gives a negative.
  • ✗ 3 h 24 min = 3.24 h✓ 3.4 h24 ÷ 60 = 0.4.

Summary

  • Count on in jumps: to the hour, whole hours, then minutes.
  • pm → add 12 to the hour; midnight = 00 00.
  • Decimal part × 60 = minutes; minutes ÷ 60 = decimal hours.
  • Fractions of time: same units first.

If you see …

  • a time past 24 00start again from 00 00 (next day).
  • speed with clock timesconvert the duration to decimal hours.

Practice

Practice: easy, medium, hard

Easy

1
2.15 pm in 24-hour time?
Show answer

Answer 14 15

2
0.25 hours in minutes?
Show answer

Answer 15

3
10 40 + 1 h 50 min?
Show working
  1. 10 40 + 1 h = 11 40
  2. + 50 min = 12 30

Answer 12 30

Medium

1
A coach leaves at 23 15 and the journey takes 3 h 50 min. Arrival time?
Guide me

What is it asking? an end time

What do we know? start 23 15, 3 h 50

Plan hours, then minutes past midnight

Show working
  1. 23 15 + 3 h = 02 15
  2. + 50 min = 03 05

Answer 03 05

2
A train leaves at 21 50 and arrives at 06 35. How long is the journey?
Guide me

What is it asking? a duration

What do we know? two times across midnight

Plan count on in jumps

Show working
  1. 10 min + 8 h + 35 min

Answer 8 h 45 min

3
Change 2.35 hours into hours and minutes.
Guide me

What is it asking? h and min

What do we know? 2.35 h

Plan 0.35 × 60

Show working
  1. \(0.35\times60=21\)

Answer 2 h 21 min

Hard

1
A drive starts at 13 45 and ends at 17 09. Find the time taken in hours, as a decimal.
Guide me

What is it asking? decimal hours

What do we know? two times

Plan duration first, then ÷ 60

Show working
  1. 3 h 24 min
  2. \(24\div60=0.4\)

Answer 3.4

PartAnswer / workingMarksGuidance
3 h 24 minM1
3.4A1
Total: 2 marks
2
Write 48 minutes as a fraction of 3 hours.
Guide me

What is it asking? a fraction

What do we know? different units

Plan 3 h = 180 min

Show working
  1. \(\tfrac{48}{180}=\tfrac4{15}\)

Answer \(\tfrac{4}{15}\)

PartAnswer / workingMarksGuidance
\(\tfrac{4}{15}\)B1
Total: 1 mark
3
A coach leaves at 07 40, arrives at 12 16 and travels 345 km. Average speed in km/h?
Guide me

What is it asking? speed

What do we know? times and distance

Plan duration → decimal hours → divide

Show working
  1. 4 h 36 min = 4.6 h
  2. \(345\div4.6=75\)

Answer 75

PartAnswer / workingMarksGuidance
4 h 36 minB1
345 ÷ 4.6M1
75A1
Total: 3 marks

Can I do this?

Anything unticked: revise that section first. All ticked: take the quiz.

Quiz

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