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

by : $42$

 * 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.