Time.
Move between units, clocks and time zones without losing track of the day.
Convert time units · read analogue and 1224-hour clocks · use timetables · solve time-zone problems
Time uses more than one conversion scale
Time does not use powers of ten between its familiar units. An hour has 60 minutes, and a minute has 60 seconds. This is why clock notation cannot be treated like an ordinary decimal.
Use multiplication when changing to a smaller unit, because more of those units are needed to represent the same duration. Use division for a larger unit. For mixed durations, convert every part before adding, and state which unit your total uses.
Convert the units before calculating, then convert back to the form requested. Clock minutes use base 60, not base 100.
Use 1 year = 365 days for these syllabus calculations unless the question specifies otherwise. A year has 12 months; months have different numbers of days, so a month is not a fixed number of weeks.
Convert 2 days 3 hours 20 minutes into minutes.
Convert 9380 seconds into hours, minutes and seconds.
9380 = 2 × 3600 + 2180. Then 2180 = 36 × 60 + 20.
Pause and explainHow many seconds are in 2 minutes 15 seconds?
2 × 60 + 15 = 135 seconds. The 15 is already in seconds, so it is added after converting the minutes.
Read analogue, 12-hour and 24-hour times
The 12-hour clock repeats its hour numbers twice daily. The labels a.m. and p.m. identify which half of the day is intended. The 24-hour clock instead counts hours from midnight to remove that ambiguity.
Practise midday and midnight separately before using the “add 12” shortcut. Midnight is 00 00 and midday is 12 00. For afternoon and evening times after midday, adding 12 to the 12-hour hour number produces the 24-hour hour.
24-hour: 15 15
12-hour: 3:15 p.m.
The minute hand shows 15 minutes. The hour hand moves gradually between hour marks.
Midnight: 00 00 = 12:00 a.m.
Noon: 12 00 = 12:00 p.m.
For a p.m. time from 1 p.m. to 11 p.m., add 12 to the hour: 3:15 p.m. = 15 15. For an a.m. time, use a leading zero when needed: 3:15 a.m. = 03 15.
Pause and explainIs 12.30 a.m. written as 12 30 in the 24-hour clock?
No. It is half an hour after midnight, so write 00 30. 12 30 is half an hour after midday.
Durations and timetables
A duration is a gap between two times, not a subtraction of two decimal numbers. You can count forward to the next whole hour, then across whole hours, then to the finishing minutes.
This stepping method also works across midnight. For a timetable, distinguish arrival, departure and waiting time. A connection is possible only if the first arrival leaves enough time before the next departure, including any stated transfer requirement.
A journey starts at 22 45 and ends at 01 20 the next day.
Total duration = 2 hours 35 minutes. Crossing midnight changes the day; do not subtract the written clock numbers as decimals.
| Station | Train A | Train B | Train C |
|---|---|---|---|
| Central | 08 10 | 08 45 | 09 20 |
| Park | 08 34 | 09 09 | 09 44 |
| Harbour | 09 05 | 09 40 | 10 15 |
To arrive at Harbour by 09 45, the latest listed departure from Central is Train B at 08 45. Its journey lasts 55 minutes. If you reach Central at 08 30, the waiting time is 15 minutes.
Pause and explainHow long is it from 09 45 to 11 10?
15 minutes to 10 00, then 1 hour to 11 00, then 10 minutes: 1 hour 25 minutes.
Time zones: put both clocks on one basis
Places in different time zones show different local clock times at the same instant. A time difference tells you how far one clock is ahead of or behind another.
Write a simple relationship such as “destination time = home time + 3 hours”. For travel, include the actual journey duration as well as the time-zone adjustment. After changing the hour, check whether the date moved to the previous or following day.
Use the time difference supplied in the question. For these examples, City A is UTC+2 and City B is UTC+5, so B is 3 hours ahead of A.
A flight leaves A at 22 30 and takes 5 hours 40 minutes. Find arrival time in B.
- Stay on A’s clock: 22 30 + 5 h 40 min = 04 10 next day.
- Convert to B’s clock: add 3 hours.
- Arrival is 07 10 next day, local time in B.
To find a journey duration from local departure and arrival times, first convert both to the same time zone and account for their dates.
Pause and explainIf a city is 4 hours ahead, what is its time when home time is 22 00?
02 00 on the following day. Adding 4 hours crosses midnight.
Your turn. Keep the day in view.
Keep clock readings separate from durations in your working. Convert to one unit for arithmetic or show a clear count-forward timeline.
In timetable and time-zone questions, label the place and date beside each time. Finish by checking that the elapsed journey time is positive and that any arrival date agrees with crossing midnight.
Write 00 35 and 18 05 in 12-hour notation.
Reveal worked answer
A film starts at 19 48 and lasts 2 hours 37 minutes. When does it end?
Reveal worked answer
Find the time from 23 50 on Monday to 02 15 on Tuesday.
Reveal worked answer
City Y is 4 hours behind City X. A flight leaves X at 16 20 and lasts 7 hours 10 minutes. Find arrival time in Y.
Reveal worked answer
Using 365 days per year, convert 2 years 3 weeks into days.