A Circular Track Is 1000m In Circumference. Cyclist A, B And C Start At The Same Position And Race Around The Track At The Following Rates Per Minute:

A circular track is 1000m in circumference. Cyclist A, B and C start at the same position and race around the track at the following rates per minute:

Cyclist A: 700m per minute
Cyclist B: 800m per minute
Cyclist C: 900m per minute

What is the least number of minutes it must take for all three to be together again.

B gains 100 yards every minute. After 10 minutes, B has lapped A once.

C gains 100 yards on B every minute, so after 10 minutes C has lapped B.

Thus, after 10 minutes, A has gone 7 laps, B has gone 8 laps, C has gone 9 laps, and all are even again.


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