The Bird Traveling Between Two Trains Puzzle

Two train stations are 60 miles apart. At 2pm one Saturday afternoon two trains start toward each other, one from each station. Just as the trains pull out of the stations, a bird springs into the air in front of the first train and flies to the front of the second train. When it reaches the second train, it turns back and flies toward the first train. The bird continues to do this until the trains meet. If one train travels at 30 miles/hour and the other train travels at 20 miles/hour, and the bird flies at 100 miles/hour, how many miles will the bird have flown before the trains meet?