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Three athletes X, Y and Z start running around a circular track of length 60m from the same point simultaneously in the same direction at speeds of 3 m/s, 5 m/s, and 9 m/s respectively. After how long will they meet for the first time after they started running?

Correct Answer: 60 sec.
Time take by X to cover a circle = 60/3 = 20 sec Time taken by Y to cover a circle = 60/5 = 12 sec Time taken by Z to cover a circle = 60/9 sec   So every 20 sec, X will be at the starting point. Every 12 secs Y will be at the starting point. Every 60/9 sec, Z will be at the starting point. Taking their LCM, we get 60. So every 60 sec, all three will be at the starting point.  All meet for the first time at the starting point after they start moving after 60 sec.

Page and Plant are running on a track AB of length 10 metres. They start running simultaneously from the ends A and B respectively. The moment they reach either of the ends, they turn around and continue running. Page and Plant run with constant speeds of 2m/s and 5m/s respectively. How far from A (in metres) are they, when they meet for the 23rd time?

Two persons start running simultaneously around a circular track of length 300 m from the same point at speeds of 15 km/hr and 25 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions ?

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