MathDB

1

Part of 2000 Canada National Olympiad

Problems(1)

Three joggers

Source: Canada 2000, Problem 1

3/4/2006
At 12:00 noon, Anne, Beth and Carmen begin running laps around a circular track of length 300300 meters, all starting from the same point on the track. Each jogger maintains a constant speed in one of the two possible directions for an indefinite period of time. Show that if Anne's speed is different from the other two speeds, then at some later time Anne will be at least 100100 meters from each of the other runners. (Here, distance is measured along the shorter of the two arcs separating two runners.)