Today's Puzzle

The Fly and the Bicycles
Two bicyclists were facing each other with the front of their wheels exactly 20 miles apart.
Both cyclists started moving towards each other.
Cyclist A at exactly 6 mph and cyclist B at 4 mph.
However, cyclist A had a fly on his wheel.
When they started moving, the fly took off towards cyclist B traveling at 30 mph (a very fast fly!).
As soon as the fly hit cyclist B's wheel, he instantly turned back towards cyclist A still travelling at exactly 30 mph, eventually hitting cyclist A's wheel, turning back towards cyclist B and repeating the process.
Eventually the two front tires hit, squishing the fly.
If you were to add up each segment the fly flew, how far did the fly travel before getting squished?