Answer:
480 miles.
Step-by-step explanation:
Let x represent the distance between Maria's house and mountains ans r represent Maria's rate for going trip.
We have been given that there was heavy traffic on the way there, and the trip took 12 hours.
[tex]\text{Distance}=\text{Rate}\times \text{Time}[/tex]
[tex]x=12r[/tex]
We are also told that hen Maya drove home, there was no traffic and the trip only took 8 hours. Maria's average rate was 20 miles per hour faster on the trip home.
So Maria's speed while returning back would be [tex]r+20[/tex].
[tex]x=8(r+20)[/tex]
Upon equating both distances, we will get:
[tex]12r=8(r+20)[/tex]
[tex]12r=8r+160[/tex]
[tex]12r-8r=8r-8r+160[/tex]
[tex]4r=160[/tex]
[tex]r=\frac{160}{4}[/tex]
[tex]r=40[/tex]
Upon substituting [tex]r=40[/tex] in equation [tex]x=12r[/tex], we will get:
[tex]x=12r\\\\x=12(40)\\\\x=480[/tex]
Therefore, Maya live 480 miles away from the mountains.
