I've the following problem:
You are walking down the escalator to catch a subway train. The escalator itself moves at a speed of Ve meters per minute. You can walk down the escalator at a relative speed of Vy meters per minute. The length of the escalator is L meters. Trains arrive T minutes apart. Let t be the time between your arrival to the station if you stand still on the escalator and the arrival of the last train before your arrival. Assume that t is a random variable uniformly distributed between 0 and T. Return the probability of catching an earlier train if you choose to walk down the escalator instead of standing still on it.
I know that the time of travel the escalator standing still is:
s = L/Ve;
I know that the time of travel the escalator walking is:
w = L/(Ve+Vy)
How can I get the probability of catching an earlier train?