A question of time

Satvik and Agnishom decide to meet up at the library to discuss geometric probability. Each of them can reach the library at any random time between 4 pm and 5 pm.

They each decide to wait exactly 20 minutes for the other person or until 5 pm, whichever comes first.

The probability that they meet can be expressed as \(\dfrac{a}{b}\), where \(a\) and \(b\) are positive co-prime integers. Find \(a \times b\).

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