Why average speed is not the average of two speeds: a worked numerical reasoning question
Average speed over an entire journey is total distance divided by total time, not the simple average of the two speeds.
A cyclist rides 60 km at an average speed of 15 km/h, then rides a further 60 km at an average speed of 20 km/h. What is her average speed for the whole 120 km journey?
Worked solution
Correct answer: 17.1 km/h
The principle
Average speed over an entire journey is total distance divided by total time, not the simple average of the two speeds.
Steps
- Time for first leg = 60 / 15 = 4 hours.
- Time for second leg = 60 / 20 = 3 hours.
- Average speed = total distance / total time = 120 / 7 = 17.14 km/h.
Heuristic to carry forward
Never average two speeds directly when the distances covered at each speed are equal but the times are not; always convert to total distance over total time.
Why each other answer is wrong
- 17.9 km/h
- Swaps the two legs' times when weighting the speeds ((15×3 + 20×4) / 7 = 17.9), attaching each speed to the wrong leg's time.
- 17.5 km/h
- Takes the simple average of the two speeds ((15+20)/2 = 17.5), which is only valid when time, not distance, is equal at each speed.
- 20 km/h
- Uses only the faster leg's speed (20 km/h), ignoring the slower first half of the journey.
Practise more questions like this one at the Wamberry practice page.