← IGCSE / O Level Mathematics

IGCSE / O Level Mathematics · Topic 1 Number · Chapter 9 · pp. 83–84

Time

Timetables, tickets and phones mostly use the 24-hour clock so that 7 in the morning can't be confused with 7 in the evening. Time also counts in 60s, not 10s, so a calculator alone gets time sums wrong. This chapter shows how to convert between the clocks, count on from one time to another, and turn a journey's distance and speed into an arrival time.

Learning objectives

  1. Read and write times on the 12-hour clock (a.m. and p.m.) and the 24-hour clock.
  2. Convert between the two clocks, including midnight and noon.
  3. Work out the time between two times, including across midnight.
  4. Convert decimal hours to hours and minutes (and minutes to minutes and seconds).
  5. Use time = distance ÷ speed to find journey times, arrival times, distances and speeds, and allow for time zones.

Book exercises: Exercise 9.1 and Student assessments 1 and 2 (pp. 83–84).

Two ways to write the same time

🔑 Key ideas

  • 12-hour clock: the hours go 1 to 12 twice. a.m. = midnight to noon, p.m. = noon to midnight.
  • 24-hour clock: the hours go 00 to 23, always with four digits: 7 a.m. is 07 00.
  • There is no a.m. or p.m. on the 24-hour clock, and no full stop between hours and minutes.
  • Midnight is 00 00 (12 a.m.); noon is 12 00 (12 p.m.).
a.m. · morning p.m. · afternoon, evening 00 0003 0006 0009 0012 0015 0018 0021 0024 00 12 a.m.6 a.m.12 noon6 p.m.12 a.m. midnight midnight 24-hour times above the bar · 12-hour times below
One day on a line. Before noon the hours match (6 a.m. = 06 00). After noon, add 12 (6 p.m. = 18 00).

Converting between the clocks

12-hour time a.m. or p.m.? a.m.: keep the hour but 12 a.m. → 00 p.m.: add 12 but 12 p.m. stays 12 9.05 a.m. → 09 05 9.05 p.m. → 21 05
12-hour to 24-hour. Going back the other way, undo it: hours 13 to 23 take away 12 and become p.m.
12-hour24-hourWhy
7 a.m.07 00a.m.: keep 7, write it with two digits
2.30 p.m.14 30p.m.: 2 + 12 = 14
11.00 p.m.23 00p.m.: 11 + 12 = 23
12.20 a.m.00 2020 minutes after midnight
12.45 p.m.12 4545 minutes after noon

📘 Example 1 · Write 4.45 p.m. on the 24-hour clock

  1. It is p.m. and the hour is not 12, so add 12 to the hour: 4 + 12 = 16.
  2. The minutes stay the same: 45.
  3. Answer: 16 45.

📘 Example 2 · Write 00 35 on the 12-hour clock

  1. The hour is 00: this is the hour just after midnight, which the 12-hour clock calls 12.
  2. It is before noon, so it is a.m.
  3. Answer: 12.35 a.m.

🧪 Try it: 12-hour ↔ 24-hour converter

Type a 12-hour time with a.m. or p.m. (such as 12.20 am), or a 24-hour time (such as 18 05).

    ✏️ Try it

    1. Write 6.50 p.m. on the 24-hour clock.
    2. Write 23 15 on the 12-hour clock.
    3. Write 12.05 a.m. on the 24-hour clock.
    Answers

    1. 18 50 · 2. 11.15 p.m. · 3. 00 05

    Next: time differences →

    Working out time differences

    🔑 Key ideas

    • There are 60 minutes in an hour, so time does not work like ordinary decimals.
    • To find the time between two times, count on: to the next whole hour, then whole hours, then the minutes left.
    • To add a time, add hours and minutes separately; every 60 minutes carries 1 hour.
    • If the end time is smaller than the start time, the journey has gone past midnight.
    13 min 3 h 15 min 09 47 10 00 13 00 13 15 13 min + 3 h + 15 min = 3 h 28 min
    Counting on from 09 47 to 13 15: jump to the next hour, then whole hours, then the leftover minutes.

    ⚠️ The calculator trap

    WorkingResult
    ✘ Wrong1315 − 947 = 368“3 h 68 min” is not a real time length
    ✔ RightCount on: 13 min + 3 h + 15 min3 h 28 min

    📘 Example 3 · How long is it from 09 47 to 13 15?

    1. Count on to the next whole hour: 09 47 → 10 00 is 13 min.
    2. Count whole hours: 10 00 → 13 00 is 3 h.
    3. Count the minutes left: 13 00 → 13 15 is 15 min.
    4. Add the pieces: 13 + 15 = 28 min, plus 3 h = 3 h 28 min.
    5. Check: 09 47 + 3 h = 12 47, + 28 min = 12 75 = 13 15. ✔

    📘 Example 4 · A night bus leaves at 21 40 and arrives at 06 15 the next day. How long is the journey?

    1. The end time is smaller than the start, so the journey goes past midnight.
    2. Count on to the next whole hour: 21 40 → 22 00 is 20 min.
    3. Count to midnight: 22 00 → 24 00 (00 00) is 2 h.
    4. Count on after midnight: 00 00 → 06 15 is 6 h 15 min.
    5. Add: 2 h + 6 h = 8 h, and 20 + 15 = 35 min, so 8 h 35 min.

    📘 Example 5 · A lesson starts at 14 48 and lasts 1 h 35 min. When does it end?

    1. Add the hours: 14 + 1 = 15.
    2. Add the minutes: 48 + 35 = 83.
    3. 83 min is more than 60: 83 = 60 + 23, so carry 1 hour. 15 h 83 min = 16 h 23 min.
    4. The lesson ends at 16 23.

    📘 Example 6 · School starts at 08 15 and the walk takes 35 minutes. What is the latest time to leave home?

    1. Count back 15 min from 08 15 to reach 08 00.
    2. 35 − 15 = 20 min still to count back: 08 00 → 07 40.
    3. Latest time to leave: 07 40.
    4. Check: 07 40 + 35 min = 07 75 = 08 15. ✔

    🧪 Try it: time-difference calculator

    If the end is earlier than the start, the calculator counts on into the next day.

      ✏️ Try it

      1. How long is it from 10 47 to 13 20?
      2. A film starts at 19 40 and lasts 1 h 55 min. When does it end?
      3. A ferry leaves at 22 50 and arrives at 03 05 the next day. How long is the crossing?
      Answers

      1. 13 min + 2 h + 20 min = 2 h 33 min · 2. 20 h 95 min = 21 35 · 3. 10 min + 1 h + 3 h 5 min = 4 h 15 min

      Next: journeys and speed →

      Journey times, distance and speed

      D S T Distance = speed × time Speed = distance ÷ time Time = distance ÷ speed
      Cover the letter you want. Side by side means multiply (S × T); one above the other means divide (D ÷ S, D ÷ T).

      Decimal hours are not hours and minutes

      Decimal4.8 h Split4 h + 0.8 h × 600.8 × 60 = 48 Answer4 h 48 min
      Only the decimal part is changed: multiply it by 60 to get minutes. The same trick turns decimal minutes into seconds.

      💡 4.8 hours is not 4 h 80 min, and 2.5 hours is not 2 h 50 min: it is 2 h 30 min.

      📘 Example 7 (from the book) · A train covers the 480 km from Paris to Lyon at 100 km/h. It leaves Paris at 08 35. When does it arrive?

      1. Time taken = distance ÷ speed = 480 ÷ 100 = 4.8 hours.
      2. Change the decimal part to minutes: 0.8 × 60 = 48 min, so 4 h 48 min.
      3. Add to the departure time: 08 35 + 4 h = 12 35, then + 48 min = 12 83.
      4. 83 min = 1 h 23 min, so the train arrives at 13 23.

      📘 Example 8 · How long does a 30 km lap take at 160 km/h? Answer in minutes and seconds.

      1. Time = 30 ÷ 160 = 0.1875 hours.
      2. Change to minutes: 0.1875 × 60 = 11.25 min.
      3. Change the decimal part to seconds: 0.25 × 60 = 15 s.
      4. Answer: 11 min 15 s.

      📘 Example 9 · A bus leaves at 10 20 and arrives at 12 05, averaging 48 km/h. How far does it travel?

      1. Journey time: 10 20 → 11 00 is 40 min, 11 00 → 12 00 is 1 h, 12 00 → 12 05 is 5 min: 1 h 45 min.
      2. Write it as decimal hours: 45 min = h = 0.75 h, so 1.75 h.
      3. Distance = speed × time = 48 × 1.75 = 84 km.

      📘 Example 10 · A car leaves at 13 50 and arrives at 16 10, after 175 km. Find its average speed.

      1. Journey time: 13 50 → 14 00 is 10 min, 14 00 → 16 10 is 2 h 10 min: 2 h 20 min.
      2. As hours: 20 min = = h, so 2 h = h.
      3. Speed = distance ÷ time = 175 ÷ = 175 × = 75 km/h.
      4. Check: 75 × = 175 km. ✔

      Time zones

      🔑 Key ideas

      • Work out the arrival time in the departure city's time first.
      • Then change it to local time: ahead → add hours; behind → take hours away.

      📘 Example 11 · A plane leaves Bangkok at 23 30 for a 13-hour flight to London. In winter London is 7 hours behind Bangkok. What is the local time in London when it lands?

      1. Arrival in Bangkok time: 23 30 + 13 h = 36 30.
      2. 36 is past 24, so it is the next day: 36 30 − 24 h = 12 30 (next day, Bangkok time).
      3. London is 7 hours behind: 12 30 − 7 h = 05 30 London time.

      ✏️ Try it

      1. How long does a 150 km journey at 40 km/h take? Answer in hours and minutes.
      2. A cyclist rides for 2 h 15 min at 16 km/h. How far does she go?
      3. A train leaves at 09 50 and travels 210 km at 60 km/h. When does it arrive?
      Answers

      1. 150 ÷ 40 = 3.75 h = 3 h 45 min · 2. 16 × 2.25 = 36 km · 3. 210 ÷ 60 = 3.5 h = 3 h 30 min, so 13 20

      Next: summary and quiz →

      Chapter summary

      • a.m. = midnight to noon, p.m. = noon to midnight. 24-hour times use four digits: 07 00, 14 30, 23 00.
      • 12-hour → 24-hour: a.m. keep the hour (12 a.m. → 00); p.m. add 12 (12 p.m. stays 12).
      • Time between two times: count on to the next hour, then whole hours, then minutes. Don't subtract like decimals.
      • Adding times: every 60 minutes carries 1 hour; past 24 00 is the next day.
      • Time = distance ÷ speed. Change the decimal part of an hour to minutes by × 60.
      • Time zones: find the arrival time at home first, then add (ahead) or subtract (behind).

      📄 Practice questions

      The book's Exercise 9.1 and Student assessments 1 and 2 are in the printable assignment for this chapter.

      Mini-quiz

      1. Write 3.45 p.m. on the 24-hour clock.
      2. What is 00 20 on the 12-hour clock?
      3. Which 24-hour time is 12.15 p.m.?
      4. A film starts at 19 40 and lasts 1 h 55 min. When does it end?
      5. How long is it from 10 47 to 13 20?
      6. How long is it from 22 15 to 05 40 the next day?
      7. How many minutes are there in 0.6 of an hour?
      8. How long does a 210 km journey at 60 km/h take?
      9. A cyclist rides for 2 h 15 min at 16 km/h. How far does she go?
      10. A train leaves at 10 10 and arrives at 11 40 after 150 km. What is its average speed?
      11. School starts at 08 30 and the walk takes 25 min. What is the latest time to leave?
      12. Bangkok is 7 hours ahead of London. It is 15 00 in Bangkok. What time is it in London?

      Source: Cambridge IGCSE Mathematics Core and Extended (4th edition, Pimentel and Wall), Chapter 9 (Time). Explanations, the Try it answers, the tools and the quiz are Guru Jazzy's own. This page is not made or endorsed by Cambridge or Hodder Education.