Logic Puzzles

# The Puzzle Of The Runners

Difficulty:

Two men ran a race round a circular course, going in opposite directions.
Brown was the best runner and gave Tompkins a start of one-eighth of the
distance. But Brown, with a contempt for his opponent, took things too easily
at the beginning, and when he had run one-sixth 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 simple conditions.

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 simple conditions.

While Brown has only run

^{1}/_{6}or^{4}/_{24}of the course, Tompkins has run the remainder^{5}/_{6}, less^{1}/_{8}, or^{17}/_{24}. Therefore Tompkins's pace is^{17}/_{4}times that of Brown. Brown has now^{5}/_{6}of the course to run, whereas Tompkins has only^{1}/_{6}. Therefore Brown must go five times as fast as Tompkins, or increase his own speed to five times^{17}/_{4}, that is,^{85}/_{4}times as fast as he went at first. But the question was not how many times as fast, but "how much faster," and^{85}/_{4}times as fast is equal to^{81}/_{4}times faster than Brown's original speed. The correct answer is therefore 20^{1}/_{4}times faster, though in practice probably impossible.See also:

• The Escalator (Difficulty: 4)

• Exploring The Desert (Difficulty: 4)

• Market Transactions (Difficulty: 5)

• What Is The Time? (Difficulty: 3)

• Reductions In Price (Difficulty: 2)

• The Runner's Refreshment (Difficulty: 4)

• The Staircase Race (Difficulty: 4)

• Sharing A Bicycle (Difficulty: 5)