I am waiting for two friends to arrive at my house. The time until A arrives is

exponentially distributed with rate a, and the time until B arrives is exponentially

distributed with rate b. Once they arrive, both will spend exponentially

distributed times, with respective rates a and b at my home before departing.

The four exponential random variables are independent.

(a) What is the expected time of the last departure?

I'd like to ask how to solve this problem?