Time questions at KS3 maths test your ability to convert between the 12-hour and 24-hour clock, calculate how long a journey takes, and read information from bus and train timetables. Time does not use the decimal system — 60 minutes make an hour — so you cannot treat it like a normal number.
What is the difference between 12-hour and 24-hour clock?
The 12-hour clock runs from 12:00 midnight to 11:59 am (morning), then restarts at 12:00 noon and runs to 11:59 pm (evening). The suffix am (ante meridiem) means before midday; pm (post meridiem) means after midday.
The 24-hour clock runs continuously from 00:00 (midnight) to 23:59 (one minute before the next midnight). No am/pm is needed.
| 12-hour time | 24-hour time | Notes |
|---|---|---|
| 12:00 midnight | 00:00 | Start of the day |
| 7:30 am | 07:30 | Morning, add leading zero |
| 12:00 noon | 12:00 | Both are the same |
| 1:45 pm | 13:45 | Add 12 for pm times (except 12 pm) |
| 11:59 pm | 23:59 | End of the day |
Converting pm to 24-hour: add 12 to the hours (except 12 pm, which stays as 12:00). Converting 24-hour (13:00–23:59) to 12-hour: subtract 12 and add pm.
How do you convert between 12-hour and 24-hour clock?
Worked example 1: Convert 3:40 pm to 24-hour time.
3:40 pm → 3 + 12 = 15 → 15:40
Worked example 2: Convert 21:15 to 12-hour time.
21:15 → 21 − 12 = 9 → 9:15 pm
Worked example 3: Convert 12:25 am to 24-hour time.
12:25 am is in the first hour after midnight → 00:25 (subtract 12 from the hour when it is 12 am).
The trickiest cases are 12:00 am (midnight = 00:00) and 12:00 pm (noon = 12:00). These are worth memorising.
How do you calculate a time interval (duration)?
A time interval is how long something lasts. Because time is based on 60 (not 10 or 100), you cannot just subtract normally without taking care.
Method 1 — counting on: Start at the start time and count forward to the finish time in stages.
Worked example 4: A film starts at 6:45 pm and finishes at 9:10 pm. How long is it?
- 6:45 pm to 7:00 pm = 15 minutes
- 7:00 pm to 9:00 pm = 2 hours
- 9:00 pm to 9:10 pm = 10 minutes
- Total = 2 hours and 25 minutes
Method 2 — convert to minutes: Convert both times to the number of minutes since midnight, subtract, then convert back.
6:45 pm = 18 hours 45 minutes = 18 × 60 + 45 = 1125 minutes 9:10 pm = 21 hours 10 minutes = 21 × 60 + 10 = 1270 minutes Difference = 1270 − 1125 = 145 minutes = 2 hours 25 minutes ✓
How do you read a bus or train timetable?
A timetable shows departure or arrival times for different stops in columns, with stops listed in rows (or vice versa). Read the column for the service you want, then find the row for your stop.
Worked example 5: Use this extract to answer questions.
| Stop | Bus A | Bus B | Bus C |
|---|---|---|---|
| Town Centre | 08:10 | 09:05 | 10:30 |
| Station | 08:22 | 09:17 | 10:42 |
| Park Road | 08:35 | — | 10:55 |
| Airport | 08:58 | 09:40 | 11:18 |
A dash (—) means the bus does not stop there.
(a) How long does Bus A take from Town Centre to Airport? 08:58 − 08:10 → count on: 08:10 to 08:58 = 48 minutes.
(b) Which is the fastest bus from Town Centre to Airport? Bus A: 48 min. Bus B: 09:40 − 09:05 = 35 min. Bus C: 11:18 − 10:30 = 48 min. Bus B is fastest (35 minutes).
(c) A passenger arrives at Station at 09:20. Which is the next bus to Airport? Bus A leaves Station at 08:22 (already gone). Bus B leaves Station at 09:17 (already gone). Bus C leaves Station at 10:42. Bus C is the next bus.
What common mistakes should you avoid?
| Mistake | Example | Correct approach |
|---|---|---|
| Subtracting times like decimals | 9:10 − 6:45 = 2.65 hours | Count on in stages; use the 60-minute rule |
| Forgetting pm adds 12 | 3:30 pm → 3:30 in 24-hr | 3:30 pm → 15:30 |
| Confusing 12 am and 12 pm | 12 am = noon | 12 am = midnight (00:00); 12 pm = noon (12:00) |
| Ignoring dashes in timetables | Assuming a bus stops everywhere | A dash means the bus skips that stop |
Frequently asked questions
Why does time use 60 rather than 100?
The 60-based (sexagesimal) system for time comes from ancient Babylonian mathematics. It has practical advantages: 60 is divisible by many small numbers (1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30), making it easy to split an hour into equal fractions without leftover pieces.
How do I calculate an arrival time if I know the start time and duration?
Add the duration to the start time. Work in hours and minutes separately, then adjust if the minutes exceed 60. For example, 10:45 plus 1 hour 30 minutes: 10 + 1 = 11 hours; 45 + 30 = 75 minutes = 1 hour 15 minutes. Total: 11 hours + 1 hour 15 minutes = 12:15.
Can I use a calculator for time questions?
Most scientific calculators have a time (degrees, minutes, seconds) function, often labelled DMS or °′″. This can help with converting between hours and minutes. However, for timetable reading and the counting-on method, mental arithmetic is usually faster and less prone to button errors.
What is the difference between "duration" and "interval"?
Both words refer to how long something takes. In GCSE maths, "time interval" is the more precise term — it is the amount of time between a start point and an end point. "Duration" tends to be used in everyday language to mean the same thing. In the exam, both words mean: find the difference between two times.
For step-by-step KS3 number and time problem support — visit aitutors.me.