Question

A person drove 36 miles per hour on a trip. If he had driven 48 miles per hour he would have arrived 4 hours earlier. What was the distance the person drove?

Answer 1

d = 576

Explanation

Think of the two different speeds as belonging to 2 different cars going to the same place, taking the same route and going to the same place.

Let the time traveled by the fast car = t

Let the time traveled by the slower car = t+4

Let the rate of travel of the slow car = 36 mph

Let the rate of travel of the fast car = 48 mph

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d = 36*(t + 4)

d = 48 * t

Since the distance is the same, they can be equated.

48t = 36(t + 4) Remove the brackets.

48t = 36t + 144 Subtract 36t from both sides.

48t - 36t = 144 Combine

12t = 144 Divide by 12

t = 144/12

t = 12

Therefore the faster car takes 12 hours to get where it is going.

d = 48 * t

d = 48 * 12

d = 576