No flies on von Neumann

The following puzzle was put to von Neumann (1903 - 1957), who had a reputation for calculating fabulously quickly: two cyclists are cycling towards each other, starting twenty miles apart, and cycling at a steady 10 m.p.h. A fly meanwhile starts from the nose of one cyclist, and flies at a steady 15 m.p.h. to the nose of the other cyclist, and then back to the first, and so on, until the cyclists meet. How far does the fly travel ? Von Neumann gave the correct solution instantly, whereupon the poser said, in a disappointed tone of voice, " Oh, you know the trick ! " Replied von Neumann, " What trick ? I just added up the infinite series ! "