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Cambridge IGCSE0607

Time

International Mathematics 0607 Chapter Notes

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Time
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In this chapter

  1. 1Units of time
  2. 2Hours and minutes are not decimals
  3. 3The 24-hour and 12-hour clock
  4. 4Journey times and times of arrival
  5. 5Reading timetables
  6. 6Time zones and time differences

1. Units of time

Time is measured in seconds (s), minutes (min), hours (h), days, weeks, months and years. Every calculation starts by getting all the times into the same unit.

There are 60 seconds in a minute, 60 minutes in an hour, 24 hours in a day and 7 days in a week. Take 1 year = 365 days.

To change to a smaller unit, multiply. To change to a larger unit, divide. A speed in km / h needs a time in hours, so change minutes to hours first.

1 h = 60 min = 3600 s

minutes ÷ 60 = hours

Examiner insight

“Many incorrectly multiplied the distance in km by a time in minutes rather than in hours.” “Many did not use the correct decimal time for 1 hour 20 min giving, for example 1.2 or 1.3 hours.”

Worked example 12 marks

A car travels at a speed of 90 km / h for 1 hour 20 min. Work out the distance the car travels.

  1. 1

    1 h 20 min = 11/3 h (or 80 ÷ 60) [1]

  2. 2

    distance = 90 × 4/3 = 120 km [1]

2. Hours and minutes are not decimals

A time such as 1 h 25 min is not 1.25 hours. The part after the decimal point is a fraction of an hour, not a number of minutes.

To change a decimal of an hour to minutes, multiply by 60. So 1.25 h is 1 h 15 min, and 1.875 h is 1 h 52.5 min.

To change minutes to hours, divide by 60. Keep the exact value, or the answer that follows is inaccurate.

0.25 h = 0.25 × 60 = 15 min

Examiner insight

“Too often a calculated value of the time as 1.25 hours often led to an answer of 1 hour 25 minutes, although some did realise that a conversion of .25 hours to 15 minutes was needed.” “A large number continued by reading the decimal part of their answer as minutes, giving them a final answer of 2 hours and 27.5 minutes.”

Worked example 13 marks

Kaya watches 25 minutes of a film. This is 5/26 of the film. Work out how long the whole film lasts. Give your answer in hours and minutes.

  1. 1

    25 ÷ 5 = 5 min is 1/26 of the film [1]

  2. 2

    5 × 26 = 130 min [1]

  3. 3

    130 min = 2 h 10 min [1]

3. The 24-hour and 12-hour clock

The 24-hour clock uses four digits: 3.15 a.m. is 03 15 and 3.15 p.m. is 15 15. From 1.00 p.m. onwards, add 12 to the hours.

A 12-hour clock time needs a.m. or p.m. after it. A time written without it scores 0 marks.

In 24-hour time the last two digits are minutes, so they never go above 59.

Examiner insight

“When writing a time as a 12-hour clock time, candidates need to write a.m. or p.m. as part of their answer.” “Many candidates did not write p.m. after their time and were awarded 0 marks for their answer of 6 42.”

Worked example 14 marks

(a) Work out how many hours there are in 3 days.

(b) Write 6.50 p.m. as a 24-hour clock time.

(c) Ali leaves home at 1.35 p.m. for a dentist appointment. He arrives 50 minutes later. Ali arrives 10 minutes after his appointment time. Work out his appointment time.

  1. 1

    (a) 3 × 24 = 72 hours [1]

  2. 2

    (b) 6.50 p.m. = 18 50 [1]

  3. 3

    (c) arrival: 1.35 p.m. + 50 min = 2.25 p.m. [1]

  4. 4

    appointment: 2.25 p.m. - 10 min = 2.15 p.m. (or 14 15) [1]

4. Journey times and times of arrival

To find how long something lasts, count up from the start to the next whole hour, then add the hours and minutes that remain. Across midnight, count up to midnight first, then add the time after it.

To find a finishing time, add the hours and minutes to the start time. Change a decimal time to hours and minutes before you add it.

Write a length of time as, for example, 2 h 29 min. A time period is not written as 2:29.

Examiner insight

“Almost all candidates were able to find the time taken for the journey in hours but converting that to hours and minutes and hence to a time of arrival, proved more difficult.” “A few subtracted the two times and gave 310 as their answer.”

Worked example 13 marks

Lavinia leaves home at 18 25 to go to the cinema. The cinema is 750 metres from Lavinia's home. Lavinia walks at an average speed of 5 km/h. Calculate the time Lavinia arrives at the cinema.

  1. 1

    750 m = 0.75 km [1]

  2. 2

    time = 0.75 ÷ 5 = 0.15 h = 0.15 × 60 = 9 min [1]

  3. 3

    18 25 + 9 min = 18 34 [1]

5. Reading timetables

Find the row for the place and the column for the journey. Read along the row to get the time at that place.

A blank box means the journey does not stop there. A journey time is the difference between two times on the same journey.

Check every condition in the question, such as arriving before a given time, before you choose a journey.

Examiner insight

“Others filled boxes of the timetable of when they thought the train would get to the station without fully appreciating that a blank box means the train does not stop at that station.” “In their working, many candidates showed the journey times as, for example, 2:29 (a time not a time period) instead of 2h 29m.”

Worked example 13 marks

The timetable shows three buses. Zaid must arrive in Dale before 11 00.

(a) Find the departure time from Ash of the latest bus that arrives in time.

(b) Work out the journey time of Bus A from Ash to Dale.

Bus ABus BBus C
Ash08 0509 1510 05
Brook08 4010 40
Dale09 2710 2211 12
  1. 1

    (a) Bus C reaches Dale at 11 12, too late; Bus B reaches Dale at 10 22, so the latest is the 09 15 from Ash [1]

  2. 2

    (b) 08 05 to 09 00 is 55 min, then 27 min more [1]

  3. 3

    55 + 27 = 82 min = 1 h 22 min [1]

6. Time zones and time differences

Places in different time zones have different local times at the same moment. The time difference is the number of hours between them.

A place that is ahead has a later local time, so add the difference. A place that is behind has an earlier local time, so subtract it.

For a journey, work out the arrival time in the departure place's time first. Then apply the time difference once.

Examiner insight

“There were a few where the 8 hour time difference was subtracted rather than added on.” “The main error here was in forgetting the 6 hours difference and obtaining a value of 14 hrs 17 mins instead of 8 hrs 17 mins.”

Worked example 13 marks

A flight leaves Town A at 21 40 local time. It lands in Town B at 08 15 local time the next day. Town B is 5 hours ahead of Town A. Work out the flight time.

  1. 1

    Town A is 5 h behind, so subtract: 08 15 - 5 h = 03 15 in Town A's time [1]

  2. 2

    21 40 to midnight is 2 h 20 min [1]

  3. 3

    midnight to 03 15 is 3 h 15 min, so the flight time is 2 h 20 min + 3 h 15 min = 5 h 35 min [1]

Recap

  • 60 s = 1 min, 60 min = 1 h, 24 h = 1 day, 7 days = 1 week, 1 year = 365 days.
  • Minutes to hours: divide by 60. Decimal of an hour to minutes: multiply by 60.
  • 24-hour clock: four digits, 3.15 p.m. is 15 15. 12-hour clock: always a.m. or p.m.
  • Journey time: count to the next whole hour, then add. Never subtract the times as ordinary numbers.
  • Timetable: a blank box means no stop. Journey time is a difference of two times.
  • Time zones: ahead means add the difference, behind means subtract it.

End-of-chapter exercise

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

  1. Change 3.4 hours into minutes.1 mark
  2. A film lasts 135 minutes. Write this length of time in hours as a decimal.2 marks
  3. Do not use a calculator. How many minutes are there in 2 days?2 marks
  4. Write 21 30 as a 12-hour clock time.1 mark
  5. Do not use a calculator. A lesson starts at 13 50 and lasts 1 hour 25 minutes. Find the time the lesson ends.2 marks
  6. Do not use a calculator. A train leaves at 09 48 and arrives at 12 15. Work out the journey time.2 marks
  7. Do not use a calculator. The timetable shows three buses. Mia must be at the Library by 15 30. (a) Find the departure time from Park of the latest bus that gets her there in time. (b) Work out the journey time of that bus from Park to the Library. | | Bus 1 | Bus 2 | Bus 3 | | --- | --- | --- | --- | | Park | 13 40 | 14 25 | 15 05 | | Market | 14 05 | 14 50 | | | Library | 14 38 | 15 24 | 15 41 |3 marks
  8. A flight leaves Town P at 22 15 local time on Monday. The flight takes 9 hours 50 minutes. Town Q is 7 hours behind Town P. Find the local time and the day when the flight lands in Town Q.4 marks
  9. Do not use a calculator. Ferry A sails 54 km at an average speed of 24 km / h. It leaves the port at 22 50 on Friday. Ferry B leaves the same port at 23 35 on Friday and takes 1 hour 40 minutes to reach the same place. Find which ferry arrives first, and by how many minutes.4 marks
  10. A plane flies 6270 km from City X to City Y at an average speed of 760 km / h. It leaves City X at 19 45 local time on Wednesday. The local time in City Y is 6 hours ahead of City X. (a) Find the local time and the day when the plane lands in City Y. (b) The plane stays in City Y for 2 hours 35 minutes and then flies back. It lands in City X at 15 20 local time on Thursday. Work out the time taken for the flight back. Give your answer in hours and minutes.6 marks

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