Suppose that a professor schedules a meeting with two students, with meeting time (in hours) modeled as iid random variables, each exponentially distributed with parameter 3. The first student is on time, but the second student is 5 minutes late. If the first student has not finished his meeting by the time the second student arrives, the second student waits for the first to finish. What is the cumulative distribution function of the random variable $R$, which is the time between the arrival of the first student and the departure of the second student?
I've tried using the law of total probability and a maximum function, but I can't get either to work out. Any tips? Note that this is homework, so please don't totally solve the problem.