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?

A and B must meet every 32 mins at the starting point as A does 4 laps to every 3 of B. So C and D have to arrive at the starting point at a similar time which is also a multiple of 32 mins. C laps at 12 mins and  after 96 mins will be at the starting point at the same time as A and B meet for the 3rd time. D starts 400m from the starting point and it will take him five and one third mins to get there and he will have done 2 more complete laps after a total of 32 mins. He will then do 3 laps every 40 mins and after a total of 192 mins D will arrive at the starting point at the same time as ABC meet there for the second time.

hughmac

Posted by hugh on 2006-04-14 04:52:00