Question 993575: Jina drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took
12
hours. When Jina drove home, there was no traffic and the trip only took
8
hours. If her average rate was
20
miles per hour faster on the trip home, how far away does Jina live from the mountains?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! rate * time = distance.
let r = rate going to the mountains.
let r + 20 = rate coming back from the mountains.
going time = 12 hours, so rate * time = distance becomes:
rate * 12 = distance
coming back time = 8 hours, so rate * time = distance becomes:
(rate + 20) * 8 = distance.
let r = rate and d = distance and your formulas become:
r * 12 = d
(r + 20) * 8 = d
simplify the second equation to get:
r * 8 + 20 * 8 = d
simplify it further to get:
r * 8 + 160 = d
your two equations are now:
r * 12 = d
r * 8 + 160 = d
subtract the second equation from the first equation and you get:
r * 4 - 160 = 0
add 160 to both sides of the equation to get:
r * 4 = 160
divide both sides of the equation by 4 to get:
r = 40
if r = 40, then r + 20 = 60
she traveled at 40 miles per hour going and 60 miles per hour coming back.
12 * 40 = 480
8 * 60 = 480
distance is 480 miles.
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