Three friends A, B and C regularly jog in 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. One day they decided to find out if they set out together in the same direction from a point what would be the fastest time for all of them to meet at any point on the track. What did they conclude?

The second day C decides to run in the opposite direction from the starting point. When will they all meet? Will this be sooner than the time taken on day one? Where do they meet in both cases?

A and C meet every 24 mins at the starting point as A does 3 laps to every 2 of C. This is the only time and place A and C meet-every 24 mins at the starting point. Therefore it is simply a matter of checking when B will arrive at the starting point at a time which is a multiple of 32mins which is 96 mins(9 laps @ 10mins 40 secs).

On the second day A and B meet every 32 mins at the starting point as A does 4 laps to every 3 of B. As this is the only time and place they meet (every 32 mins at the starting point) it is simply a matter of finding a time C will be at the starting point which is a multiple of 32 mins which is 96 mins(8 laps @ 12mins).

On both days they all meet at the starting point after 96 minutes.

Posted by hugh on 2006-04-18 23:52:58