The total distance

A Ferrari is traveling at 30 miles per hour on a head-on collision course with a Maserati, which is being driven at a leisurely 20 miles per hour. When the two cars are exactly 50 miles apart, a very fast fly leaves the front fender of the Ferrari and travels towards the Maserati at 100 miles per hour. When it reaches the Maserati, it instantly reverses direction and flies back to the Ferrari and continues winging back and forth between the rapidly approaching cars. At the moment the two cars collide, what is the total distance the fly has covered?

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At first glance it may seem that a horrendous calculation is necessary to solve this; the sum of an infinite series of numbers that get smaller and smaller as the cars approach each other. But if you focus on time rather than distance, a solution is easy. The cars are 50 miles apart and traveling towards each other at a combined speed of 50 miles per hour, so they will meet in one hour. In that hour, a fly that flies at 100 miles per hour will naturally travel 100 miles.

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