Nibble or Nosh?

From Detectograms And Other Puzzles by F. Gregory Hartswick (sweet name):

Once upon a time there was a stretch of road 20 miles long. At each end of this road lived a bicyclist, and at exactly the same instant, they started riding toward each other at a constant speed of 10 mph, continuing until their front wheels touched. At the moment they started, a fly, perched on the front wheel of one of the bikes, started to fly toward the other at a constant speed of 15 mph. He flew until the touched the front wheel and instantly started back, always with the same speed, till he touched the front wheel of the first, and so on, flying back and forth between the wheels until eh was crushed as they met. Each journey naturally was shorter than the one before.

Now: Exactly how far did the fly fly?

Note: Due to both his excessive nerdiness and the excessive regularity with which he checks this blog, Jason Houle is hereby banned from solving the above puzzle, or at least answering it in a comment.