Three friends A, B and C regularly jog in a circular jogging track every morning. The track is 1000 m in circumference.

A takes 8 mins to complete one lap, B takes 10 mins and 40 secs and C takes 12 mins. All of them setout from a same point but C runs in the opposite direction from starting point.

Another friend D joins this run. D normally takes 13 mins and 20 secs to complete one lap. He decides to run in the same direction as C but from a point 600 m ahead of C in his jogging direction. When will they all meet each other on the circular track & where?

(In reply to re: solution by Kevin K-C)

The way salil has set it up is so that for example A is travelling at 1/480 revolutions per second while B is travelling at 1/640 revolutions per second.  That means that A is traveling relative to B at 1/1920 revolutions per second, meaning that he meets B every 1920 seconds. But this is exactly 4 times the time it takes for A to go around the track itself once; since 4 is an integer, they always meet at the starting point.

Other angular velocities would have different results. The solutions didn't include any assumptions beyond what is forced by the puzzle itself.

Posted by Charlie on 2006-04-14 09:18:56