A Bird And 2 Crashing Trains Problem

There is a problem in the 5th edition of a Physics textbook by Resnick, Halliday and Krane that I found very interesting, and I would like to share it with you. What is unique about it is that there are two ways about to solving it, a correct more complex way, and a seemingly correct (but incorrect in reality) simple method. I will show you both method later, but for now I will just say it demonstrates a pitfall with relative frames of reference. Try to solve it by yourself at first!

Two trains, each having a speed of 34 km/h, are headed toward each other on the same straight track. A bird that can fly 58 km/h flies off the front of one train when they are 102 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.

a) How many trips can the bird make from one train to the other before the trains crash?

b) What is the total distance the bird travels?