Two cars and a bird

Two cars, setting out from points A and B are 140 miles apart. They move toward each other on the same perfectly straight road, until they collide at C. Their speeds are 30 mph and 40 mph. At the very instant they start, a bird takes flight from point A heading straight toward the car which has left point B. As soon as the bird reaches the other car, it turns and changes direction. The bird flies back and forth between the two cars at a speed of 50 mph until the cars collide.

How long is the birds total flight path?

Assume that the bird do not lose time when it changes its direction

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