Will They Ever Meet?

Discrete Mathematics Level 4

Sasha and Joel are pen pals, who have never met, and are making an appointment in a restaurant during "lunch time."

However, due to their unspecific timing, each of them will randomly come into their meeting place between 12:00 to 13:00 P.M.

Each of them will wait for his or her partner for 10 minutes, but if the other party doesn't show up within that time frame, the date is over immediately.

If the probability for this couple to meet each other can be written as \(\dfrac{a}{b}\), where \(a\) and \(b\) are coprime positive integers, compute \(a+b\).


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