Question

Lena drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 7 hours. When Lena drove home, there was no traffic and the trip only took 5 hours. If her average rate was 18 miles per hour faster on the trip home, how far away does Lena live from the mountains? Do not do any rounding.

Answer 1

The distance between Lena's house and mountains is 315 miles.

Step-by-step explanation:

We know that average speed is given by

`Speed=(Distance)/(Time)`

Let the distance between the house of Lena and mountains be 'd'

Let the speed of trip towards mountains be
`vmph`

`\therefore v=(d)/(t_(1))=(d)/(7)...........(i)`

Since the average speed on the trip home is given as
`18+v` thus we have

`v+18=(d)/(t_(2))\\\\\therefore v+18=(d)/(5)..............(ii)`

Solving equations i and ii for 'd' we get

`(d)/(7)+18=(d)/(5)\\\\(d)/(5)-(d)/(7)=18\\\\(2d)/(35)=18\\\\\therefore d=9* 35=315miles`