Lapping a slower runner

Question

Two runners start together at the same point on a 400 metre circular track. One runs at 8 m/s, the other at 6 m/s. 1. If they run in the same direction, after how long does the faster runner first pass the slower one (lap him)? 2. If they run in opposite directions, how often do they meet? 3. In the same-direction case, how many times will they have met after the faster runner completes 10 laps?

Accepted Answer

Same direction: first lapping after 200 seconds. Opposite directions: they meet every 28.6 seconds. After 10 laps by the faster runner there have been 2 lappings. Same direction. The faster runner gains on the slower at 8 minus 6 = 2 m/s. To lap him, the faster runner must gain a full lap, 400 m. That takes 400 / 2 = 200 seconds, by which time the faster has run 1,600 m (4 laps) and the slower 1,200 m (3 laps). Opposite directions. Now they approach each other at 8 + 6 = 14 m/s, and they meet every time their combined distance reaches 400 m: every 400 / 14, about 28.6 seconds. After ten laps.…

Lapping a slower runner

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