Uniform distribution: 2 friends meeting between 1pm 2pm

Two friends decide to meet at the Diamond Plaza between 1 pm and 2 pm. They cannot meet before 1 pm or after 2 pm. The one who comes to the meeting point first must wait 10 minutes for the other one. If the other person does not show up within 10 minutes, then he can leave. For example, A comes first at 1:13. He waits till 1:23. If B does not show before 1:23, then A leaves the meeting point. Assuming that the distribution of time of arrival between 1 pm and 2 pm is uniform for both persons, what is the probability that they will meet?

Here is an example of your problem except the times are 12 to 1 instead of 1 to 2 and they wait 20 minutes instead of 10. Other than that it is the same problem. Just change the values.

http://www.cs.uleth.ca/~sheriff/statist ... 4_soln.pdf