Three runners start together from one point of a 600 m track and run the same way at 4 m/s, 6 m/s and 9 m/s. After how many seconds will all three first be together again, anywhere on the track?

Question

Accepted Answer

600 s. The 4 and 6 m/s runners meet every 600/2=300 s; the 6 and 9 m/s runners every 600/3=200 s. All three together: LCM(300, 200) = 600 s.

Three runners start together from one point of a 600 m track and run the same way at 4 m/s, 6 m/s and 9 m/s. After how many seconds will all three first be together again, anywhere on the track?

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