Runner 200 m behind: 300 and 250 m/min

On a straight path, one runner is 200 m behind another. They start at the same time and run in the same direction at 300 m/min and 250 m/min. After how many minutes does the faster runner catch up?

Step-by-step

1. 300 − 250 = 50
   Moving the same way, the relative speed is the difference of the speeds
2. 200 ÷ 50 = 4
   Catch-up time = distance ÷ relative speed

Why it works

Running in the same direction, the faster runner gains on the slower one at the difference of their speeds, so the time to close a 200 m lead is that lead divided by the speed difference.

Common mistakes

• Adding the speeds instead of subtracting them.
• Dividing 200 m by the 300 m/min speed alone.

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