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

Answer:

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

Explanation:

We know that average speed is given by

$Speed=\frac{Distance}{Time}$

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

Let the speed of trip towards mountains be $vmph$

$\therefore v=\frac{d}{t_{1}}=\frac{d}{7}...........(i)$

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

$v+18=\frac{d}{t_{2}}\\\\\therefore v+18=\frac{d}{5}..............(ii)$

Solving equations i and ii for 'd' we get

$\frac{d}{7}+18=\frac{d}{5}\\\\\frac{d}{5}-\frac{d}{7}=18\\\\\frac{2d}{35}=18\\\\\therefore d=9\times 35=315miles$