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Probability of seeing your friend

Updated: Aug 2, 2023

Two best friends, Alice and Kim, will go to the same coffee shop anytime between 2pm and 3pm on the same day, and each one will stay there at most A minutes and then leave. None of them will be there before 2pm and none of them will stay there after 3pm. If the maximum probability for them to see each other at the coffee shop between 2pm and 3pm is 50%, what is A?


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