Two boys on bicycles, 87 miles apart, began racing directly toward each other. The instant they started, a fly on the handle bar 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 flew back and forth in this way, from handle bar to handle bar, until the two bicycles met.
If each bicycle had a constant speed of 15 miles an hour, and the fly flew at a constant speed of 16 miles an hour, how far did the fly fly?