MathDB

B3

Part of 1971 Putnam

Problems(1)

Putnam 1971 B3

Source:

4/6/2022
Two cars travel around a track at equal and constant speeds, each completing a lap every hour. From a common starting point, the first starts at time t=0t=0 and the second at an arbitrary later time t=T>0.t=T>0. Prove that there is a total period of exactly one hour during the motion in which the first has completed twice as many laps as the second.
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