Sung drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 10 hours. When Sung drove home, there was no traffic and the trip only took 7 hours. If his average rate was 18 miles per hour faster on the trip home, how far away does Sung live from the mountains? Do not do any rounding.

Sung drove to the mountains

s₁=speed when Sung drove to the mountains.

t=10 hour.

d=distance.

s₁=d/t

s₁=d/10 hour ⇒s₁=d/10 (1)

Sung drove home:

s₂=speed when Sung drove home.

t=7 hour

s₂=s₁+18 miles/hour

s₂=d/7 hour ⇒s₁+18 miles/h=d/7 hour ⇒ s₁+18=d/7 (2)

Whit the equations (1) and (2) make a system of equations:

s₁=d/10

s₁+18=d/7

we can solve this system of equations by substitution method.

d/10+18=d/7

least common multiple=70

7d+1260=10d

7d-10d=-1260

-3d=-1260

d=-1260/-3=420

Answer: distance = 420 miles.