SOLUTION: Elsa drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 8 hours. When she drove home, there was no traffic and the trip took 6 hours.

Question 878872: Elsa drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 8 hours. When she drove home, there was no traffic and the trip took 6 hours. If her average rate was 16 mph faster on the trip home, how far away does Elsa live from the mountains?
Found 2 solutions by lwsshak3, josmiceli:
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Elsa drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 8 hours. When she drove home, there was no traffic and the trip took 6 hours. If her average rate was 16 mph faster on the trip home, how far away does Elsa live from the mountains?
***
let x=rate of speed on the way to the mountain
x+16=rate of speed on the way home
distance=travel time*rate of speed
..
8x=6(x+16)
8x=6x+96
2x=96
x=48
distance=8*48=384
how far away does Elsa live from the mountains? 384 miles
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = her ave rate going to mountains in mi/hr
Let = her ave rate driving back in mi/hr
Let = the one-way distance to mountains
---------------
(1)
(2)
(3)
-----------------
Substitute (2) and (3) into (1)
(1)
Multiply both sides by
(1)
(1)
(1)
(1)
----------------
(2)
(2) mi/hr
and
(1)
(1) mi/hr
Her ave rate going to mountains was 48 mi/hr
Her ave rate driving back was 64 mi/hr
-----------------------
check:
(1)
(1)
(1)
OK

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