The Fly’s Final Commute

Two trains are travelling toward each other along the same straight track. At the start, the fronts of the trains are 120 kilometres apart, and each train moves at a constant speed of 40 kilometres per hour. A fly begins on the front of one train and immediately flies toward the other at 70 kilometres per hour. Whenever it reaches a train, it reverses direction instantly and flies back toward the other one. It continues shuttling between the approaching trains until their fronts meet. Assuming the fly never pauses and maintains the same speed throughout, what total distance does the fly travel?