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Commuter trains leave from middletown for centerville every hour on the hour. The triptakes 3 hours. Each train waits at the centerville train depot for a half hour and then returns to middletown. If the return trip also takes 3 hours, how many trains will each train pass (going in the oposite direction) during the round trip?

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What have you tried so far? –  Daryl Dec 16 '12 at 4:12
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The train travels at one direction for 3 hours and each train leaves in 1hour intervals with the same speed. The trains are going at opposite directions. So, the speed they approach to one another doubles-- within the 3 hour period, a train sees 6 trains in the opposite direction. If those other trains were stationary on the road, the train would see 3 of them. But they are no the road at every hour to get into the 3-hour period the train is travelling. Same thing in both directions-- adds up to 12.

Getting into the numbers, suppose the train leaves middletown at noon to arrive at 3:30. The period 12:00-3:30 is the period the trains to travel back to centerville during the intervals 9:30-12:30, 10:30-1:30, ..., 2:30-5:30 are on the road and that's 6 of them. The train sees them all. Same thing for the other direction.

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Hint: When train x leads Middletown, how many trains are on the way there from Centerville? Train x will pass each of them, plus those that leave Centerville in the next 3 hours. Is the situation symmetrical going both ways?

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What did you add to your original answer in the edit Dan Christensen ? –  ashley Dec 16 '12 at 19:13
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