A car travels between two towns 120 miles apart. It starts from rest, accelerates uniformly to a maximum speed, maintains this speed for a certain distance, and then decelerates uniformly to rest. If the car reaches a maximum speed of 60 miles per hour and the total travel time is 2.5 hours, determine the distance over which the car maintains its maximum speed. Let's think step by step and output the final answer within \boxed{}.
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