(no subject)

Why is it that on weeknights, I never have enough time to do everything that I want to get done and I stay up too late to do them, but come Friday night I just want to sleep?

Time to wake those brains

Marvin leaves work at random times between 3 and 5 PM. His mother lives uptown, his girlfriend lives downtown. Uptown and downtown trains arrive at his station with equal frequency. He takes the first subway that comes in either direction and eats dinner with the one he is first delivered to. His mother complains that he hardly ever comes to dine with her, but he says it's a 50-50 chance. He has had dinner with his mother twice in the last 20 working days. Explain.

(And no, the answer is not that he is lying to his mother so he could spend more time with his girlfriend. Let's keep our minds out of the gutters.)

SOLUTION:
The trip length was irrelevant. What was important was the time the subways left the station. The train to Mom probably arrived a very short time after the train to GF, making it more likely that he would catch the train to GF.

If the train to Mom always arrived two minutes after the train to GF, then he has a much better chance of catching the train to GF. Say, if both trains arrived every half-hour, and the train to GF always arrived at the top and bottom of the hour, and the train to Mom always arrived two minutes after the top and bottom of the hour. If he arrives at the station between 4:00 and 4:02, then he will take the train to Mom. If he arrives at the station between 4:03 and 4:30, then he will take the train to GF.