Problem Page 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 hours. If her average rate was miles per hour faster on the trip home, how far away does Lashonda live from the mountains?

Answer: 420 miles away

Step-by-step 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