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?

(In reply to A start? by tomarken)

A travels at 1/480 rev/sec
B travels at 1/640 rev/sec
C travels at 1/720 rev/sec

The difference between A's and B's angular velocities is 1/1920 rev/sec, so A meets B every 1920 seconds.

The difference between A's and C's angular velocities is 1/1440 rev/sec, so A meets C every 1440 seconds.

The LCM of 1920 and 1440 is indeed 5760, so indeed they do meet after 5760 seconds (that is, 96 minutes), at the starting point.

The second day, when C is running in the opposite direction, his speed is added to that of A, rather than subtracted, so their relative speed is 1/480+1/720 = 1/288.

The LCM of 1920 and 288 is also 5760, so they all meet on the second day again after 96 minutes.

Posted by Charlie on 2006-04-12 10:49:51