Question

Suppose a family drives at an average rate of 60 miles an hour on the way to visit relatives and then at rate of 40 miles an hour on the way back. The return trip takes 1 hour longer than the trip there. Let D be the distance in miles the family traveled. How many hours did it take to drive there?

Answer 1

3 hours

Explanation:

`speed = (distance)/(time) \\ 60 = (d)/(t) \\ d = 60t \\ \\ speed = (distance)/(time) \\ 40 = (d)/(t + 1) \\ d = 40(t + 1)`

Since;

`d = 60t \: \: \: and\\ d = 40(t + 1) \\`

Therefore;

`60t = 40(t + 1) \\ 60t = 40t + 40 \\ 60t - 40t = 40 \\ 20t = 40`

Divide both sides by 20

`(20t)/(20) = (40)/(20) \\ t = 2 \: hours`

Since the return trip took an hour longer to get back home an hour will be added to the time

`t + 1 = 2 + 1 \\ = 3 \: hours`