MathDB

Leaving his house at noon, Jim walks at a constant rate of

4

miles per hour along a

4

mile square route returning to his house at

1

PM. At a randomly chosen time between noon and

1

PM, Sally chooses a random location along Jim's route and begins running at a constant rate of

7

miles per hour along Jim's route in the same direction that Jim is walking until she completes one

4

mile circuit of the square route. The probability that Sally runs past Jim while he is walking is given by

\frac{m}{n}

, where

m

and

n

are relatively prime positive integers. Find

m + n

Problem Statement