Step 1 :Let $x$ be the number of hours the train ride lasted. The total distance of the trip would be the sum of the distance covered by the train and the distance covered by the car. The distance covered by each can be calculated by multiplying the time spent on each by their respective speeds. Since the total time spent is 8 hours, the time spent on the car would be 8 - x hours.
Step 2 :The total distance of the trip, in miles, can be expressed as \(76x + 51(8 - x)\).
Step 3 :Simplify the expression to get the final answer: \(\boxed{25x + 408}\)