Highway 66 Fly I

Highway $66$, which is a one-lane road of length $300$ miles, has Lightning McQueen and Tow Mater racing towards each other. They start at opposite ends of the road. Lightning McQueen and Tow Mater respectively drive towards at each at constant rates of $90$ miles per hour and $45$ miles per hour. A fly starts on Tow Mater and flies towards Lightning McQueen at a rate of $135$ miles per hour. Then, once it hits Lightning McQueen, it immediately starts to fly back to Tow Mater at the same rate. This repeats until Lightning McQueen and Tow Mater crash into one another. Assuming the fly repeats this pattern and doesn't fly out of the way before the cars crash, how many miles will the fly travel in total?