Two trains 10 miles apart travel toward each other at, one at 6mph, the other 4mph. A fly goes back and forth between their headlights at 13 mph until they meet.
How far does the fly travel? (nearest 1/10 mile)
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edndori
ANSWERS: 1
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There are two approaches to solving this problem: (1) Construct an infinite series of each leg of the fly's flight, involving shorter and shorter lengths over shorter and shorter times, and compute the sum of the series; (2) Short-cut: Compute how long until the trains collide and multiply by the fly's speed. This is a famous problem. According to http://mathworld.wolfram.com/TwoTrainsPuzzle.html: When posed with a variant of this question involving a fly and two bicycles, [legendary mathematician] John von Neumann is reputed to have immediately answered with the correct result. When subsequently asked if he had heard the short-cut solution, he answered no, that his immediate answer had been a result of explicitly summing the series.
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