The Bulldozers and the Bee

Problem
Two (presumably driven by a pair of insane enemies) are $20$ miles apart, heading towards each other at $10$ miles per hour, on a collision course.

At the same time, a takes off from the  of one bulldozer at $20$ miles per hour, towards the other bulldozer.

As soon as the bee reaches the other bulldozer, it reverses direction instantaneously and heads off at $20$ miles per hour back towards the first bulldozer.

It continues to do this until the bulldozers collide, squashing the bee between them and killing her.

The question is: how far does the bee fly before the collision?

Solution
This is frequently asked as a trick question.

The Short Answer
The bulldozers are travelling at $10$ mph and are $20$ miles apart.

Therefore they travel $10$ miles each and collide after $1$ hour.

The bee is flying at $20$ mph and therefore travels $20$ miles in that time.

Pointless quibbles
Whether a bee can actually fly at $20$ miles per hour is doubtful, let alone sustain that speed for a whole hour. I may be completely wrong. This may be completely reasonable.

Even if she could, she could not reverse direction instantaneously. The laws of physics are completely against it.