TT2008 Junior O-Level - P5
Source:
September 4, 2010
geometryperimetercombinatorics proposedcombinatorics
Problem Statement
On a straight track are several runners, each running at a di fferent constant speed. They start at one end of the track at the same time. When a runner reaches any end of the track, he immediately turns around and runs back with the same speed (then he reaches the other end and turns back again, and so on). Some time after the start, all runners meet at the same point. Prove that this will happen again.