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One complete lap around a particular circular track is 500 meters. Jun and Quan each start running at the starting line and run around the track; Jun runs clockwise at 2 meters per second, and Quan runs counterclockwise at 4 meters per second. When they meet for the sixth time after starting, they stop and both walk back together along the track to the starting line. What is the shortest distance they could walk back on the track together?

Sep 27, 2020

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One complete lap around a particular circular track is 500 meters. Jun and Quan each start running at the starting line and run around the track; Jun runs clockwise at 2 meters per second, and Quan runs counterclockwise at 4 meters per second. When they meet for the sixth time after starting, they stop and both walk back together along the track to the starting line. What is the shortest distance they could walk back on the track together?

Hello Guest!

$$(2+4)\frac{m}{s}\cdot t=500m\\ t=\frac{500}{6}s$$

$$t=83.\overline{3}s$$

$$83.\overline{3}s\cdot 6\cdot 4\frac{m}{s}=2000m\\ 83.\overline{3}s\cdot 6\cdot 2\frac{m}{s}=1000m$$

Jun and Quan meet at the starting point for their sixth meeting.

!

Sep 27, 2020
edited by asinus  Sep 27, 2020