Henry Ernest Dudeney/Modern Puzzles/42 - The Puzzle of the Runners

Modern Puzzles by Henry Ernest Dudeney: $42$

The Puzzle of the Runners

Two men ran a race round a circular course, going in opposite directions.

Brown was the best runner and gave Tompkins a start of $\tfrac 1 8$ of the distance.

But Brown, with a contempt for his opponent, took things too easily at the beginning,

and when he had run $\tfrac 1 6$ of his distance he met Tompkins,

and saw that his chance of winning the race was very small.

How much faster than he went before must Brown now run in order to tie with his competitor?

The puzzle is quite easy when once you have grasped its initial conditions.

Sources

• 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Arithmetical and Algebraical Problems: Locomotion and Speed Puzzles: $42$. -- The Puzzle of the Runners
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Speed & Distance Puzzles: $70$. The Puzzle of the Runners