Consider a one-way road where the cars form a PP(lambda) with rate lambda cars/sec. The road is x feet wide. A pedestrian, who walks at a speed of u feet/sec, will cross the road if and only if she is certain that no cars will cross the pedestrian crossing while she is on it. Shwo that the expected time until she completes the crossing is (e^{x/u}-1)/lambda

All I know is that it will take x/u seconds to cross. Not sure how to start the problem...