Catch-up: 400 m behind at 90 and 70 m/min

Jia starts 400 m behind Yi, and both walk in the same direction, Jia at 90 m/min and Yi at 70 m/min. How many minutes does Jia need to catch up?

Step-by-step

1. 90 − 70 = 20
   Moving the same way, the relative speed is the difference of the speeds
2. 400 ÷ 20 = 20
   Catch-up time = distance ÷ relative speed

Why it works

Walking the same way, Jia gains on Yi only at the difference of their speeds, so the time to close the 400 m gap is the gap divided by that difference.

Common mistakes

• Adding the two speeds (that is the head-on meeting case).
• Dividing the 400 m gap by Jia's own speed.

Related

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