# 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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