Question

A person drove 65 miles per hour on a trip. If he had driven 78 miles per hour, he would have arrived 4 hours earlier. What was the distance the person drove?

Answer 1

To find the distance the person drove, set up a system of equations using the given information. Solve the equations to find the distance driven.

Step-by-step explanation:

To find the distance the person drove, we can set up a system of equations. Let x be the distance driven in miles, and let t be the time travelled in hours. We are given two pieces of information:

1. At a speed of 65 mph, the person arrived t hours later than if they had driven at 78 mph. So, we have the equation: x/65 = x/78 - t

2. The difference in time is 4 hours. So, we have the equation: t = 4

Now, we can solve these equations to find the distance the person drove.

Simplifying the first equation, we get: 78x = 65x - 65 * 4

Combining like terms, we have: 13x = 260

Dividing both sides by 13, we get: x = 20

Therefore, the person drove a distance of 20 miles.