# Geometric Probability at the Airport

**Discrete Mathematics**Level 3

A taxi arrives at an airport between \(3:00\) and \(4:00\) to wait for a particular man. It will wait for ten minutes, and if the man doesn't come, it will leave. That same man will get off his flight at anywhere from \(2:50\) to \(3:40\). It will take him ten minutes to walk to were he can catch his taxi. He will wait twenty minutes for the taxi. If the taxi doesn't show up, he will rent a car and drive home. Let \(\frac{a}{b}\) be the probability that the man has to rent a car where \(a\) and \(b\) are coprime, positive integers. Find \(a+b\).