A famous story about the outstanding mathematician John von Neumann (1903–1957) concerns the following problem: Two bicyclists start 20 miles apart and head toward each other, each going 10 miles per hour. At the same time, a fly traveling 15 miles per hour leaves the front wheel of one bicycle, flies to the front wheel of the other bicycle, turns around and flies back to the wheel of the first bicycle, and so on, continuing in this manner until trapped between the two wheels. What total distance did the fly fly? There is a quick way to solve this problem. However, von Neumann allegedly solved this problem instantly by summing an infinite series. Solve this problem using both methods.