From one point of a 720 m circular track, Anuj and Badal run clockwise at 6 m/s and 4 m/s while Chetan runs anticlockwise at 3 m/s, all starting together. After how many minutes are all three together again for the first time?

Question

Accepted Answer

12 min. Anuj and Badal meet every 720/6-4=360 s; Anuj and Chetan every 720/6+3=80 s; Badal and Chetan every 720/7 s. The first common time is LCM(360, 80) = 720 s, which is also 7×720/7. So 720 s = 12 min.

From one point of a 720 m circular track, Anuj and Badal run clockwise at 6 m/s and 4 m/s while Chetan runs anticlockwise at 3 m/s, all starting together. After how many minutes are all three together again for the first time?

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