Sheet № 115 · Foundation + Higher · AQA · Edexcel · OCR
Speed, Distance & Time Calculations –
Speed, distance and time problems appear on almost every GCSE Maths paper. Whether the question involves a car journey, a runner, or a distance-time graph, the same core formula applies. This guide takes you through the formula triangle, unit conversions, average speed, and how to interpret distance-time graphs, with fully worked examples
§Key definitions
Question:
A cyclist travels 45 km in 3 hours. What is the cyclist's average speed?
Answer:
The average speed is 15 km/h.
Q1 (Foundation):
A runner covers 800 metres in 2 minutes 30 seconds. Calculate the speed in m/s.
Q2 (Foundation):
How far does a car travel in 45 minutes at a speed of 60 km/h?
Q3 (Higher):
A bus travels 24 km at 32 km/h, then 36 km at 48 km/h. Find the average speed for the whole journey.
§Formulas to memorise
Speed = Distance ÷ Time
Distance = Speed × Time
Time = Distance ÷ Speed
To convert km/h to m/s, multiply by 1000 ÷ 3600 (or divide by 3.6)
Identify — which quantity you need to find (speed, distance, or time).
Check units — make sure distance and time units are consistent with the speed units.
Substitute — into the correct rearrangement of the formula.
Calculate — and include the correct unit in your answer.
Worked example
A cyclist travels 45 km in 3 hours. What is the cyclist's average speed?
Working: Speed = Distance ÷ Time Speed = 45 ÷ 3 = 15 km/h.
⚠ Common mistakes
- ✗Averaging the two speeds directly. Average speed = total distance ÷ total time, not the mean of the individual speeds. The worked example above shows why.
- ✗Using minutes instead of hours. If time is given as 2 hours 15 minutes, convert to 2.25 hours before dividing. Do not use 2.15.
- ✗Forgetting unit conversions. If speed is in m/s and distance is in km, convert km to metres first, or convert speed to km/h.
✦ Exam tips
- →Always state the formula you are using — this earns a method mark even if the arithmetic goes wrong.
- →On distance-time graph questions, remember that the gradient of a line gives the speed. A steeper line means a faster speed.
- →A horizontal section on a distance-time graph means the object is stationary (speed = 0).
- →When converting minutes to hours, divide by 60 — not by 100. For example, 45 minutes = 0.75 hours, not 0.45.