Problem 7. The Traveling Bee

Two trains leave two towns that are fifty miles apart. They travel toward each other at rates of 30 mph and 20 mph respectively. A bumblebee flying at the rate of 50 mph starts out just as the faster train departs the train station, and flies to the slower train. The bee then turns around and goes back to meet the faster train. Then it turns around again, etc., and it keeps flying back and forth between the trains until the trains meet. How far does the tired bumblebee fly?