Answer: 420 miles away
Explanation:
Lashonda drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 10 hours. When Lashonda drove home, there was no traffic and the trip only took 7 hours. If her average rate was 18 miles per hour faster on the trip home, how far away does Lashonda live from the mountains?
one to mountains:
s = x miles
t = 10h
v₁ = x/10
Back home
s = x miles
t = 7h
v₂ = x/7
And we know that v₂ = v₁ + 18. So, we have:
v₂ = v₁ + 18
v₁ = x/10 → x = 10v₁
v₂ = x/7 → x = 7v₂
10v₁ = 7v₂ → v₁ = 7v₂/10
v₂ = v₁ + 18
v₂ = 7v₂/10 + 18
10v₂ = 7v₂ + 180
10v₂ - 7v₂ = 180
3v₂ = 180
v₂ = 60 mi/h
v₂ = x/7 → x = 60.7 = 420 miles