Henry Ernest Dudeney/Puzzles and Curious Problems/79 - A Cycle Race/Solution

by : $79$

 * A Cycle Race

Solution

 * $12$ minutes.

Proof
After $4$ minutes, Robinson has completed one circuit, while Brown is $\dfrac 1 3$ the way round his first circuit.

After $8$ minutes, Robinson has completed two circuits, while Brown has completed $1 \tfrac 1 3$ circuits, but Robinson has not yet caught up with Brown.

After $12$ minutes, Robinson has completed $3$ circuits, while Brown has just about completed $2$ circuits, which is the point Robinson overtakes Brown.