Two people agree to meet at a coffee shop. they each independently pick a random moment in time between 8
a. m. and 9
a. m. and show up exactly at their selected time. but they are very impatient, and only stay for 10 minutes after when they arrive. what is the probability that they meet? express your answer as a common fraction.

Since the time scheduled is from 8 am to 9 am, therefore the two people have a 1 hour allowance to meet. This means that there are a total of 60 minutes that we have to work on.

The total number of possibilities that person 1 shows up and person 2 shows up is both bounded by 0 minute to 60 minutes respectively. Where 0 minute refers to the time at 8 am and 60 minutes refer to 9 am.  So we see that they can show up anytime between the boundaries. So the total possibility is:

Total possibilities = 60 * 60 = 3600

Since they are both impatient, therefore this means the two have less than 10 minutes to work on. So the region bounded by the time when they do not meet is from 0 minute to 50 minutes. Therefore the total possibility of them not meeting is:

Possibilities of not meeting = 50 * 50 = 2500

Therefore the possibilities of meeting is:

Possibilities of meeting = 3600 – 2500 = 1100

Hence the probability they meet is:

Probability of meeting = 1100 / 3600 = 11/36

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