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(10 Points) Two mathematicians take a morning coffee break each day. They arrive at the cafeteria independently, at random times between 9 a.m. and
(10 Points) 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. Find the value of m such that the probability that either one arrives while the other is in the cafeteria is 0.4.
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