1998 AIME Problem 9

Two mathematicians take a morning coffee break each day. They arrive at the cafeteria independently, at random times between 9 a.m. and 10 a.m., and stay for exactly m minutes. The probability that either one arrives while the other is in the cafeteria is 40 \%, and m=a-b \sqrt{c}, where a, b, and c are positive integers, and c is not divisible by the square of any prime. Find a+b+c.