Numerical aptitude · Time and motion
Races and circular tracks, made easy
💡 The idea
A race is speed, time and distance with two runners. The trick: look at where the loser is at the moment the winner finishes.
🏃 A finishes 100 m→🏃 B is at 90 m→A wins by 10 m
🧭 The method: 3 steps
- Find the winner’s time to finish.
- Find how far the other runner gets in that time.
- The gap is the winning margin. On a round track: same way → subtract speeds; opposite → add.
🎬 Every kind of question, in pictures
Pick a kind. Guess the answer first, then watch the picture work it out. Tap any step to see it in the picture.
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✏️ Worked examples
Example 1. 100 m race: A 10 m/s, B 8 m/s. A wins by?
- A finishes in 100 ÷ 10 = 10 s
- B runs 8 × 10 = 80 m
- A wins by 20 m
Example 2. 400 m track, 7 m/s and 3 m/s, same way. When do they meet?
- The faster gains 7 − 3 = 4 m/s
- Meet when it gains a whole lap: 400 ÷ 4 = 100 s
⚠️ Where people go wrong
- Using the difference in speed as the winning margin.
- On a circular track, opposite directions ADD the speeds.
📌 Remember
- Margin = distance − loser’s distance at the winner’s time
- Same way: lap ÷ (a − b)
- Opposite: lap ÷ (a + b)