The Fast Bee Puzzle

Two trains 140 miles apart are traveling at 70 miles per hour on a collision course. A bee, traveling at 80 miles per hour, leaves the front of the first train and flies to the front of the second train, turns around without losing any speed, returns to the first train, turns around without losing any speed, flies to the second train, and continues in this pattern until it is smashed in the collision. How far does the bee travel before its demise?

The answer...