Lap race: 400 m track, 150 and 100 m/min

On a 400 m circular track, two runners start together from the same point and run in the same direction at 150 m/min and 100 m/min. After how many minutes does the faster runner first catch up with the slower one?

Step-by-step

1. 150 − 100 = 50
   Moving the same way, the relative speed is the difference of the speeds
2. 400 ÷ 50 = 8
   Catch-up time = distance ÷ relative speed

Why it works

To catch up on a lap, the faster runner must gain exactly one full lap; the gain each minute is the difference of the speeds, so the time is the lap length divided by that difference.

Common mistakes

• Adding the speeds as if they ran toward each other.
• Dividing the 400 m lap by the faster runner's own speed.

Related

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