average velocity question

[olilee]

I am having a little trouble starting this problem for physics class.
Two trains, each having a speed of 30 km/h, are headed at each other on the same straight track. A bird that can fly 60 km/h flies off the front of one train when they are 60 km apart and heads directly for the other train. On reaching the other train it flies directly back to the first train, and so forth. What is the total distance the bird travels?
I am assuming that the bird travels till the two trains meet in the middle since their velocity is the same. But I am not sure how to approach the question. Thank you so much in advance for the help.

[humanino]

Yeah it is so well-known :cool:
Just use the simplest formula for distance : you already know one variable, what is the value of the other ?

[humanino]

There is a story that tells, Von Neumann has been asked this problem. After thinking for one or two minutes, he gives the correct answer. The other guy very surprised : "Weird ! Usually people try to sum the series instead of using the simple solution !" Von Neumann replies "What simple solution ?" :biggrin:

I hope it's fake. :bugeye:

[HallsofIvy]

There is an old story that a person asked VonNeumann a problem similar to this. VonNeumann thought for a moment and then gave the correct answer. The questioner laughed and said "Most people start trying to do that as an infinite sum!".
VonNeumann looked puzzled and said "But I did it as an infinite sum!"

For those of us who can't do such sums in our head, there is a much simpler way to do it: the trains are headed toward each other at 30 km/h and so are "closing" on each other at 60 km/h., they will colide after 1 hour. (Another way to calculate that is to argue that since the trains have the same speed, they will meet in the middle {just as you said}- each must cover 30 km at 30 km/h so- 1 hour.)

Now you know the bird will be flying at 60 km/h for one hour. How far will it have flown?