Problem #99: The Bicycles and the Fly

Two boys on bicycles 20 miles apart, began racing directly toward each other. The instance they started, a fly on the handle of one bicycle started flying straight toward the other cyclist. As soon as it reached the other handle bar it turned and started back. The fly went back and forth this way, from handle bar to handle bar, until the two bicycles met.

If each bicycle 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 fly?

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