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Cambridge IGCSE0580

Time

Mathematics 0580 Chapter Notes

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Time
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In this chapter

  1. 1Units of time
  2. 2Decimal hours
  3. 3Time differences and adding time
  4. 4The 24-hour clock
  5. 5The 12-hour clock
  6. 6Events that repeat
  7. 7Time zones
  8. 8Reading timetables

1. Units of time

Time is measured in seconds (s), minutes (min), hours (h), days, weeks, months and years. Know how the units relate: 60 seconds in a minute, 60 minutes in an hour, 24 hours in a day and 7 days in a week.

Use 1 year = 365 days. To change hours to minutes, multiply by 60. To change minutes to hours, divide by 60.

hours × 60 = minutes

minutes ÷ 60 = hours

1 year = 365 days

Examiner insight

“Some divided by an incorrectly converted time value for 1 hour 15 minutes, commonly 1.15.”

Worked example 12 marks

A bus takes 1 hour 15 minutes to travel 45 km between two towns. Work out the average speed of the bus in kilometres per hour.

  1. 1

    change the time to hours: 1 h 15 min = 1 + 15/60 = 1.25 h [1]

  2. 2

    speed = 45 ÷ 1.25 = 36 km/h [1]

2. Decimal hours

A time such as 2.65 hours is not 2 hours 65 minutes. The whole number is the hours. Turn the decimal part into minutes by multiplying by 60, so 2.65 hours is 2 hours 39 minutes.

To go the other way, divide the minutes by 60. Keep the decimal exact before you round.

0.65 h = 0.65 × 60 = 39 min

2 h 39 min = 2 + 39/60 = 2.65 h

Examiner insight

“The most common error in the time was the incorrect decimalisation to 4.3 hours.”

Worked example 13 marks

Sam leaves home at 14 30 and drives 106 km to town A. His average speed is 40 km / h.

Calculate the time he arrives at town A.

  1. 1

    time = 106 ÷ 40 = 2.65 h [1]

  2. 2

    0.65 × 60 = 39, so the journey takes 2 h 39 min [1]

  3. 3

    14 30 + 2 h 39 min = 17 09 [1]

3. Time differences and adding time

Never subtract or add times as if they were decimals. There are 60 minutes in an hour, not 100.

The safest method is to go through the next whole hour. Add on to the earlier time rather than subtract. Add up the pieces to get the length of time.

To work back from a finishing time, add up the lengths first. Then subtract the total.

08 20 to 09 00 to 11 00 to 11 15: 40 + 120 + 15 = 175 min

Examiner insight

“Candidates should be encouraged to add on to the earlier time rather than subtract, which often led to using 100 minutes in an hour, hence 23 40 – 06 50 = 16 90.” “Candidates should have a strategy for dealing with time differences, as many resort to a subtraction sum without taking into account that there are 60 minutes in each hour rather than 100.”

Worked example 12 marks

When Ahmed gets out of bed he takes 12 minutes to get dressed, 26 minutes to eat breakfast and 37 minutes to walk to the station.

Ahmed must be at the station by 09 45.

Work out the latest time Ahmed can get out of bed.

  1. 1

    total time = 12 + 26 + 37 = 75 min = 1 h 15 min [1]

  2. 2

    09 45 - 1 h 15 min = 08 30 [1]

4. The 24-hour clock

The 24-hour clock writes every time with four digits: two for the hours, then two for the minutes. For example, 3.15 a.m. is 03 15 and 3.15 p.m. is 15 15.

For a time after noon, add 12 to the hour. For a time before noon, the hour stays the same. Keep every zero. Five past one in the afternoon is 13 05, not 13 5 or 1 05.

A 24-hour time never has a.m. or p.m. after it.

4.25 p.m.: 4 + 12 = 16, so 16 25

Examiner insight

“Many candidates did not gain the accuracy mark for the answer as they did not write the time correctly in the 24-hour clock form, with 13 5 being very common, along with 01 05 and 1 05.” “Some answers were written in 12-hour clock but omitted the ‘pm’, or were written in 24-hour clock and included a ‘pm’.”

Worked example 11 mark

Write 4.25 pm using the 24-hour clock.

  1. 1

    afternoon, so add 12 hours: 4 + 12 = 16, giving 16 25 [1]

5. The 12-hour clock

The 12-hour clock needs a.m. or p.m. Without it, 4.25 could be early morning or afternoon. For a 24-hour time after 12 00, subtract 12 from the hour and write p.m.

When a calculation passes 24 00, the clock starts again at 00 00. Take the working in stages. Change each stage into an actual time before the next one.

22 15: 22 - 12 = 10, so 10.15 p.m.

Examiner insight

“The majority however, used the 12-hour system, but of these it was rare to see the essential ‘pm’ to distinguish their answers from the early morning time.” “Some confusion was evident about which system for time was intended and unfortunately those working in the 12-hour system often did not give the essential pm.”

Worked example 12 marks

Do not use a calculator. A film starts at 19 40 and lasts 2 hours 35 minutes.

Write the time the film ends, using the 12-hour clock.

  1. 1

    19 40 + 2 h = 21 40, and 21 40 + 35 min = 22 15 [1]

  2. 2

    22 - 12 = 10, so the film ends at 10.15 p.m. [1]

6. Events that repeat

Two events repeat at different gaps and happen together at the start. They next happen together after the lowest common multiple (LCM) of the two gaps.

Find the LCM in minutes. Change it to hours and minutes. Then add it to the start time.

Adding one gap to the start time is not enough.

34 = 2 × 17, 30 = 2 × 3 × 5, LCM = 2 × 3 × 5 × 17 = 510

Examiner insight

“A few added 30 and 34 mins to 0800 to give 0904.” “Some listed the times or multiples, and often had incomplete lists or arithmetic errors.”

Worked example 13 marks

Two buses leave the bus station at 08 00. One returns to the station every 34 minutes. The other returns to the station every 30 minutes.

Work out the time they will first return to the station together.

  1. 1

    lowest common multiple of 34 and 30 is 2 × 3 × 5 × 17 = 510 minutes [1]

  2. 2

    510 ÷ 60 = 8 remainder 30, so 8 h 30 min [1]

  3. 3

    08 00 + 8 h 30 min = 16 30 [1]

7. Time zones

Local times differ between places. If place A is ahead of place B, A's clock shows a later time. To get B's time from A's, subtract the difference. To get A's time from B's, add it.

Take the problem in stages. First find the arrival time in the departure place's time. Then change to the local time where the plane lands. A time past 24 00 is the next day.

time in the place that is behind = time in the place that is ahead - difference

Examiner insight

“A common error was then to add 10.5 hours to the correct arrival time in Mumbai time instead of subtracting.” “Mistakes were often made when dealing with midnight; 01 15 was a common incorrect answer resulting from losing an hour by counting 24 00 when adding either the flight time or the time difference.”

Worked example 12 marks

Nisha flies from Mumbai to New York. The journey takes 16 hours 18 minutes. The flight departs from Mumbai at 11 50. The local time in Mumbai is 10.5 hours ahead of the local time in New York.

Find the local time in New York when Nisha's flight arrives.

  1. 1

    arrival in Mumbai time: 11 50 + 16 h 18 min = 04 08 the next day [1]

  2. 2

    New York is behind, so subtract: 04 08 - 10 h 30 min = 17 38 [1]

8. Reading timetables

A timetable lists the times of each service at each stop. Read down a column for one service and across a row for one stop.

To find how long a service takes, find the times at the two stops. Then work out the difference through the next whole hour.

To be somewhere by a time, choose a service that arrives at or before it.

09 42 to 10 00 to 10 30: 18 + 30 = 48 min

Worked example 13 marks

Do not use a calculator. The table gives part of a train timetable.

(a) Find how many minutes Train 2 takes to travel from Brook to Calder.

(b) Mia leaves Ashby and must arrive at Calder by 10 00. State which train she should catch.

Train 1Train 2
Ashby08 1509 05
Brook08 5209 42
Calder09 4010 30
  1. 1

    (a) 09 42 to 10 00 is 18 min, and 10 00 to 10 30 is 30 min [1]

  2. 2

    18 + 30 = 48 minutes [1]

  3. 3

    (b) Train 1 arrives at 09 40, before 10 00. Train 2 arrives at 10 30, too late. Train 1 [1]

Recap

  • 60 seconds in a minute, 60 minutes in an hour. 1 year = 365 days.
  • Minutes to hours: divide by 60. Decimal part of an hour to minutes: multiply by 60.
  • Find a time difference by going through the next whole hour.
  • 24-hour clock: four digits, no a.m. or p.m. 3.15 p.m. is 15 15.
  • 12-hour clock: always write a.m. or p.m.
  • Events that repeat happen together after the LCM of their gaps.
  • Time zones: place ahead has the later time. Subtract to go back, add to go forward.
  • Timetable: read down for a service, across for a stop.

End-of-chapter exercise

Test yourself on the whole chapter. Work through these before moving on.

  1. Do not use a calculator. Change 3 and a half hours into minutes.1 mark
  2. Write 2.4 hours in hours and minutes.2 marks
  3. Do not use a calculator. Write 7.05 pm using the 24-hour clock.1 mark
  4. Write 00 45 using the 12-hour clock.1 mark
  5. Do not use a calculator. A lesson starts at 13 50 and ends at 15 15. Find the length of the lesson in minutes.3 marks
  6. A year has 365 days. How many full weeks are in a year, and how many days are left over?2 marks
  7. Do not use a calculator. A night train leaves at 22 40 and arrives at 03 25 the next day. Find the length of the journey.3 marks
  8. A coach leaves at 09 20 and travels 140 km at an average speed of 80 km / h. Find the time it arrives.3 marks
  9. Do not use a calculator. The local time in town P is 9 hours ahead of the local time in town Q. A plane leaves Q at 20 30 local time on Monday and takes 14 hours 20 minutes to reach P. It stays at P for 2 hours 45 minutes. It then flies back to Q, taking 13 hours 35 minutes. (a) Find the local time and the day in P when the plane lands at P. (b) Find the local time and the day in Q when the plane lands back at Q.5 marks
  10. A cargo plane flies 6020 km from city X to city Y at an average speed of 840 km / h. The local time in city Y is 5.5 hours behind the local time in city X. The plane lands in Y at 00 25 local time on Friday. Find the local time in X when the plane took off, and say which day it was. Give the time using the 12-hour clock.6 marks

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