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.
[tex]\text{Distance}}=\text{Time}\times \text{Speed}[/tex]
[tex]d=8r...(1)[/tex]
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.
[tex]d=6(r+16)...(2)[/tex]
Upon equating equation (1) and equation (2), we will get:
[tex]8r=6(r+16)[/tex]
[tex]8r=6r+96[/tex]
[tex]8r-6r=6r-6r+96[/tex]
[tex]2r=96[/tex]
[tex]\frac{2r}{2}=\frac{96}{2}[/tex]
[tex]r=48[/tex]
Upon substituting [tex]r=48[/tex] in equation (1), we will get:
[tex]d=8r\Rightarrow 8(48)=384[/tex]
Therefore, Mai lives 384 miles away from the mountains.
