Another quick puzzle

The desert getting more and more flies, don't know why. I manage to kill few with my bare hands. Found this simple puzzle, so let your brain do some exercises.

Dinstein and Wisely is cycling on the road from opposite direction. When they are exactly 20km apart, they began racing toward each other. The instant they started, a fly on the handlebar of Dinstein's bike also started flying toward Wisely. As soon as it reached the Wisely's handlebar, it turned and started back toward Dinstein. They fly flew back and forth in this way until two bicycles met. Each bicycle moved at constant speed of 10km/h and the fly flew at a constant speed of 15km/h. Find, how much distance did the fly cover?

============= Update: The solution ===============


I'd extracted this puzzle from a great story about John von Neumann. If you don't know who is John von Neumann, then you must be sleeping in the class. He is a mathematician, but I knew him because of computing. If you want to know more about this great mathematician, you can visit the wiki.

Ok, back to the story.

At a cocktail party, someone has posed this puzzle to him. Von Neumann withdrew himself to another room and figure out the answer. With a very short time, von Neumann come back with a correct answer.

For most of us will look at this as a very complicated puzzle. We will start to measure the distance that the fly flew back and forth; using integration, area under graphs, etc.

The answer given by this great mathematician to this question is very straight forward and simple.

First, calculate the time needed for both bicycle met.

time = distance / speed
time = 20km / (10 + 10)km/h
time = 1 hr.

Both Dinstein and Wisely will met after 1 hour, and the distance that the fly covered in 1 hour can be calculated as

distance = speed * time
distance = 15km/h * 1h
distance = 15km

Surprise?

Most of us tend to solve problem in very difficult and complex way, but sometime, the solution is just simple and straight forward.