Two trains, each having a speed of 25 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 57 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. (We have no idea why a bird would behave in this way.) What is the total distance the bird travels before the trains collide?
The Attempt at a Solution
I am completely stumped on this one. I think I need to add the velocities since the trains are headed in the same direction but I am confused on determining when the bird will reach the other train. It also seems like there is an infinite number of returns that will get smaller and smaller and I am unclear If I need to apply some calculus to this problem.