Tom, Dick, and Harry started out on a $100$-mile journey. Tom and Harry traveled by automobile at a speed of $25$ mph, while Dick walked at a speed of $5$ mph. After a certain distance, Harry got off and continued walking at $5$ mph, while Tom went back for Dick and brought him to the destination at the same time that Harry arrived. Find the number of hours required for the trip.

Let's think step by step and output the final answer within \boxed{}.
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