In a kilometer race, A beats B by 80 meters or by 10 seconds. What is the time…

Concept

In a race where one runner beats another “by a distance or by a time”, both descriptions refer to the SAME finishing gap. The loser still has that distance left to run when the winner finishes, and the stated time is exactly how long the loser needs to cover that leftover distance. So the leftover distance divided by the stated time gives the loser’s speed, from which the loser’s full-course time follows, and the winner’s time is that minus the time gap.

Application

1. Course length = 1000 m. When A finishes, B is 80 m behind, i.e. B has 80 m still to run, and B needs 10 s to cover those 80 m.

2. Speed of B = leftover distance ÷ leftover time = 80 m ÷ 10 s = 8 m/s.

3. Time for B to run the full 1000 m = 1000 ÷ 8 = 125 s.

4. A finishes 10 s before B, so time taken by A = 125 − 10 = 115 s.

Cross-check

Speed of A = 1000 m ÷ 115 s ≈ 8.696 m/s. In A’s 115 s, B (at 8 m/s) runs 8 × 115 = 920 m, which is exactly 80 m short of 1000 m — matching the “beats by 80 m” condition. Both clues are satisfied.

Time taken by A over the course = 115 seconds.