The absent-minded professor and the tardy student. A professor (absent-minded by convention) gives each of two students an appointment at 12 noon. One of the students arrives on time; the second arrives 5 minutes late. The amount of time the first student spends closeted with the professor is X1; the second student engages the professor as soon as he is free and spends time X2 in conference with him. Suppose X1 and X2 are independent random variables with the common exponential distribution of mean 30 minutes. What is the expected duration from the arrival of the first student to the departure of the second? [Condition on X1.]