Question

Mai drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 8 hours. When Mai drove home, there was no traffic and the trip only took 6 hours. If her average rate was 16 miles per hour faster on the trip home, how far away does Mai live from the mountains?

Answer 1

Answer:

Mai lives 384 miles away from the mountains

Step-by-step explanation:

Let d represent distance between Mai's house and mountains and r represent Mai's rate while going to mountains.

We have been given that there was heavy traffic on the way there, and the trip to mountains took 8 hours.

$\text{Distance}}=\text{Time}\times \text{Speed}$

$d=8r...(1)$

We are also told that when Mai drove home, there was no traffic and the trip only took 6 hours. Her average rate was 16 miles per hour faster on the trip home.

$d=6(r+16)...(2)$

Upon equating equation (1) and equation (2), we will get:

$8r=6(r+16)$

$8r=6r+96$

$8r-6r=6r-6r+96$

$2r=96$

$\frac{2r}{2}=\frac{96}{2}$

$r=48$

Upon substituting $r=48$ in equation (1), we will get:

$d=8r\Rightarrow 8(48)=384$

Therefore, Mai lives 384 miles away from the mountains.