Question

A person drove at a speed of 24 miles per hour on a back road during a recent trip. They can drive the same distance at 40 mph on the interstate in one hour less. What is the distance they drove on the back road?

Answer 1

The person drove a distance of 60 miles on the back road.

Step-by-step explanation:

Let's assume the distance driven on the back road is x miles.

The time taken to drive on the back road is given by t1 = x/24 hours.

The time taken to drive on the interstate is given by t2 = x/40 hours.

According to the given information, t2 is 1 hour less than t1. So we have:

1. t2 = t1 - 1

Substituting the values, we get:

1. x/40 = x/24 - 1

Simplifying the equation:

1. x/40 = x/24 - 1
2. x/40 - x/24 = -1
3. x(1/40 - 1/24) = -1
4. x(3/120 - 5/120) = -1
5. x(-2/120) = -1
6. x/(-60) = -1
7. x = 60