The Fly and the Bicycle
Two cyclists 20 miles apart began riding directly toward each other. The instance they started, a fly on the handlebar of one bicycle started flying straight toward the other cyclist. As soon as it reached the other handlebar it turned and started back. The fly went back and forth this way, from handlebar to handlebar, until the two cyclists met.
If each cyclist had a constant speed of 10 miles per hour, and the fly flew at a constant speed of 15 miles per hour, how far did the fly travel?
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Solution
If each cyclist had a constant speed of 10 miles per hour, and the fly flew at a constant speed of 15 miles per hour, how far did the fly travel?
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Solution
This problem illustrates infinite series, geometric sums, and mathematical reasoning. This problem can be written as the sum of an infinite, geometric series - although mathematical reasoning about the total length of time the fly travels produces the same answer. Frequently, mathematicians try to reduce seemingly-complex problems to simpler ones that they know how to solve; this problem is an example of an infinite-series problem being reduced to simple arithmetic.