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 $$a + b + c.$$

(第十六届AIME1998 第9题)