Time Calculations and Timetables — AQA GCSE Maths Revision Notes

What you'll learn

This topic covers working with time: adding and subtracting durations, converting between the 12-hour and 24-hour clocks, and reading a timetable. By the end of this guide you should be able to find how long something lasted and work out arrival and departure times.

You should also be able to convert between decimal hours and hours-and-minutes, use time in speed calculations, plan a journey from a timetable, and handle problems crossing midnight or involving time zones.

The organising idea is that time is not decimal, and almost every error in this topic comes from forgetting it. There are 60 minutes in an hour, not 100, so 1.5 hours is 1 hour 30 minutes while 1 hour 30 minutes entered into a calculator as 1.30 is wrong. The same trap catches subtraction: 3:10 minus 1:45 cannot be done by subtracting the digits, because borrowing gives 60 rather than 10. Treat the hours and the minutes as separate quantities in base 60, and the whole topic becomes reliable.

Key terms and definitions

12-hour clock — times from 1:00 to 12:59 with am or pm.

24-hour clock — times from 00:00 to 23:59, always four digits.

am — before midday. pm — after midday.

Duration — how long something lasts, as opposed to when it happens.

Decimal hours — a time expressed as a decimal, such as 2.25 hours for 2 hours 15 minutes.

Timetable — a table of times, usually with each service in its own column.

Core concepts

The units

There are 60 seconds in a minute, 60 minutes in an hour, 24 hours in a day and 7 days in a week.

The sixties are what make time different from every other measurement at GCSE. Metric units convert by powers of ten, so 3.5 m is unambiguously 350 cm; time does not, so 3.5 hours is 3 hours 30 minutes rather than 3 hours 50 minutes.

Whenever a minutes figure reaches 60, convert it into an hour. An answer containing "75 minutes" as part of a time is not finished.

The 12-hour and 24-hour clocks

The 24-hour clock runs from 00:00 to 23:59 and is always written with four digits, so five past nine in the morning is 09:05.

To convert an afternoon 12-hour time into 24-hour, add 12 to the hours: 3:40 pm becomes 15:40.

To convert back, subtract 12 from any hour above 12: 19:25 becomes 7:25 pm.

Two special cases catch people out. 12:00 midday is 12:00 in both systems, but 12:00 midnight is 00:00 and belongs to the following day. And 12:30 am is 00:30, not 12:30, because the hour after midnight is the zero hour.

Adding and subtracting times

Work in two parts, hours and minutes, and carry or borrow in sixties.

To add 2 hours 45 minutes to 09:50: the minutes give 50 + 45 = 95, which is 1 hour 35 minutes, so carry the hour. The hours give 9 + 2 + 1 = 12, and the answer is 12:35.

To find the duration from 14:20 to 17:05: the minutes would need 5 − 20, so borrow an hour, making it 65 − 20 = 45 minutes, and the hours become 16 − 14 = 2. The duration is 2 hours 45 minutes.

A calculator handles neither of these directly, which is why the working must be done in two parts.

Counting on

An often easier method for durations is to count on in convenient jumps, usually to the next whole hour first.

From 14:20 to 17:05: 40 minutes takes you to 15:00, then 2 hours takes you to 17:00, then 5 minutes gives 17:05. Total: 2 hours 45 minutes.

This avoids borrowing altogether and is less error-prone under pressure. It also works naturally across midnight.

Crossing midnight

Where a duration spans midnight, split it at 00:00.

A shift from 21:30 to 06:15 runs 2 hours 30 minutes to midnight, then 6 hours 15 minutes after it, giving 8 hours 45 minutes.

Subtracting the two times directly gives a negative answer, which is the signal that the period crosses midnight and needs splitting.

Decimal hours

Speed, distance and time calculations need decimal hours, since dividing by "2 hours 30 minutes" is meaningless to a calculator.

To convert minutes into a decimal, divide by 60: 30 minutes is 0.5 hours, 15 minutes is 0.25, and 20 minutes is one third, so 0.333 recurring.

Going back, multiply the decimal part by 60: 3.75 hours is 0.75 × 60 = 45 minutes, so 3 hours 45 minutes.

The error to avoid is treating the digits after the point as minutes. A journey of 2.4 hours is 2 hours 24 minutes, not 2 hours 40 minutes.

Time in speed calculations

Speed is distance divided by time, and the time must be in the units the answer needs.

A car covering 150 km in 2 hours 30 minutes has a speed of 150 ÷ 2.5 = 60 km/h. Dividing by 2.30 would give 65.2, which is simply wrong.

Going the other way, a time that comes out as a decimal usually needs converting back for the final answer: a journey time of 1.8 hours is 1 hour 48 minutes.

Reading timetables

Each column is normally one service, and each row is a stop, so a journey is read down a single column.

The duration of a journey is the arrival time minus the departure time, calculated as above.

Waiting time at a change is the departure of the next service minus the arrival of the first.

Two conventions matter. A dash or blank means the service does not stop there, so that column cannot be used for that stop. And services are usually listed in time order across the page, which makes "the next bus after 10:15" a matter of reading along the row.

Questions often ask for the latest train someone can catch to arrive by a given time, which means working backwards up the column from the arrival requirement.

Calendar calculations

Some questions involve days, weeks and months rather than hours.

There are 7 days in a week, 52 weeks in a year, and 365 days in an ordinary year — 366 in a leap year, which occurs when the year divides by 4, except for century years that do not divide by 400.

Month lengths vary between 28 and 31 days, so counting days across a month boundary means splitting the calculation: from 25 March to 8 April is 6 days remaining in March plus 8 in April, giving 14 days.

Questions about repeating events use factors and multiples: two tasks done every 4 and every 6 days coincide every 12 days, which is their lowest common multiple.

Time zones

Where a question involves two places, apply the difference before or after the journey as the situation requires.

A flight leaving London at 10:00 and lasting 8 hours arrives at 18:00 London time. If the destination is 5 hours behind, the local arrival time is 13:00.

State which time zone each figure is in as you work, since mixing them is the usual source of error.

Worked examples

Example 1: A duration crossing midnight

A nurse's shift runs from 20:45 to 07:30. How long is the shift?

The times cannot be subtracted directly, since the period crosses midnight.

From 20:45 to 21:00 is 15 minutes, and from 21:00 to midnight is 3 hours, so 3 hours 15 minutes to midnight.

From midnight to 07:30 is 7 hours 30 minutes.

Total: 3 hours 15 minutes plus 7 hours 30 minutes = 10 hours 45 minutes.

The minutes came to 45, under 60, so no carrying was needed. The shift is 10 hours 45 minutes.

Example 2: Decimal hours in a speed calculation

A train travels 210 km in 2 hours 48 minutes. Find its average speed in km/h.

Convert the time to decimal hours: 48 ÷ 60 = 0.8, so the time is 2.8 hours.

Speed = 210 ÷ 2.8 = 75 km/h.

Dividing by 2.48 would have given 84.7, an error of nearly 10 km/h caused entirely by treating the minutes as decimals.

Example 3: Working backwards from a timetable

A meeting starts at 14:00 and the office is a 25-minute walk from the station. Trains arrive at 13:05, 13:20, 13:38 and 14:05. Which is the latest train that gets someone there on time?

Work backwards from the requirement: arriving by 14:00 after a 25-minute walk means leaving the station by 13:35.

The 13:38 train arrives too late to walk and be on time, and the 14:05 arrives after the meeting has started.

The latest usable train arrives at 13:20, giving 15 minutes to spare.

Checking forwards confirms it: 13:20 plus 25 minutes is 13:45, comfortably before 14:00.

Common mistakes and how to avoid them

Treating time as decimal. 1 hour 30 minutes is 1.5 hours, not 1.30.

Subtracting times digit by digit. Borrow in sixties: borrowing an hour gives 60 minutes, not 10.

Leaving 60 or more minutes in an answer. Convert them into an hour.

Mishandling midnight. 12:00 midnight is 00:00 and starts a new day; 12:30 am is 00:30.

Dividing by a time written as hours-point-minutes. Convert to decimal hours first.

Reading a timetable across the rows instead of down a column. Each column is one service.

Ignoring a dash in a timetable. It means that service does not stop there.

Exam technique for "Time Calculations and Timetables"

Count on to the next whole hour rather than subtracting. It avoids borrowing entirely and is faster under pressure.

Write times in the 24-hour clock throughout your working, even if the question uses am and pm, so no ambiguity remains.

Convert minutes to decimal hours as a separate written step before any speed calculation, showing the division by 60.

For timetable questions, highlight the column you are using, and work backwards up it when the question fixes an arrival time.

Give the answer in the form the question asks for — "2 hours 45 minutes" and "2.75 hours" are both right, but only one may be wanted.

Check that any minutes figure in your final answer is below 60.

Quick revision summary

Time is not decimal: 60 seconds in a minute, 60 minutes in an hour. So 1.5 hours is 1 hour 30 minutes, and 2.4 hours is 2 hours 24 minutes.

The 24-hour clock always has four digits. Add 12 to pm hours, subtract 12 to go back. Midnight is 00:00 and 12:30 am is 00:30.

Add and subtract times in two parts, carrying and borrowing in sixties — or, more reliably, count on to the next whole hour.

For a duration crossing midnight, split the calculation at 00:00.

Convert minutes to decimal hours by dividing by 60, and back by multiplying the decimal part by 60. Speed calculations need decimal hours.

In a timetable, each column is one service and a dash means no stop. Work backwards up the column when an arrival time is fixed.

Finish by checking no minutes figure in the answer reaches 60.