Problem #90: The Amorous Commuter

John Jones lives in Maidenhead. He has one girlfriend in Reading and another in Slough. He has no car and therefore takes a train whenever he goes to see them.

Trains stopping in Maidenhead can go either east or west. If they are westbound, they will go to Reading. If they are eastbound, they will go to Slough. There are an equal number of trains going in each direction.

John likes his two girlfriends equally. Because he finds it hard to choose between them, he decides that when he goes to the station, he will take the first arriving train, regardless of whether it is going east or west. After he has done this for a month, he finds that he has visited the girlfriend in Slough 11 times as often as he visited the girl in Reading. Assuming that he arrived an the Maidenhead station at random times, why should the poor girl in Reading have received so little attention?

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