there is a much easier solution to this ... note that (rate)(time) = distanceHere is the question:
"Two boys on bicycles, 35 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 13 miles an hour, and the fly flew at a constant speed of 21 miles an hour, how far did the fly fly?"
Intuitively, (I think) I see that this is describing an alternating series since the two bikes will be closer and closer and therefore the sum of the distances the fly has to travel back and forth will converge (conditionally) to a point. I just don't know how to actually solve the problem numerically and would greatly appreciate it if someone could show me how.
Thanks in advance!