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As a Fly Flies....

Two trains start at the same time in opposite directions from the ends of a five hundred-mile road. Each train speeds towards the other train at a speed of 50 miles per hour. At the start, a fly , traveling at the speed of 80 miles per hour, leaves one of the trains and flies to the other train, then flies back to the first train...flying back and forth between the trains until the two trains meet. How far did the fly travel (in miles) before he was squished between the two colliding trains?


Hint: Draw a few cases....then stop and think.


Solution Commentary: It is possible to set this up and solve it using infinite series...but, if you stopped to think....you might notice that it took 5 hours for the two trains to meet, which means that the fly traveled (80 miles/hour)(5 hours) = 400 miles.