Question 778222: Keisha drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 8 hours. When Keisha drove home, there was no traffic and the trip only took 6 hours. If her average rate was 16 miles per hour faster on the trip home, how far away does Keisha live from the mountains?
Found 2 solutions by mananth, MathTherapy:
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! Keisha drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 8 hours. When Keisha drove home, there was no traffic and the trip only took 6 hours. If her average rate was 16 miles per hour faster on the trip home, how far away does Keisha live from the mountains?
way up
distance from home = x
speed = y
time =8 hours
d=rt
x=8y
x-8y=0...............(1)
return
distance =x
speed = y+16
time = 6 hours
x=6(y+16)
x=6y+96
x-6y=96...............(2)
x -8 y = 0 .............1
x -6 y = 96 .............2
Eliminate y
multiply (1)by 6
Multiply (2) by 8
6 x -48 y = 0
8 x -48 y = 768
Add the two equations
14 x = 768
/ 14
x = 55
plug value of x in (1)
1 x -8 y = 0
55 -8 y = 0
-8 y = 0 -55
-8 y = -55
y = 7
x= 55 the distance from home
Answer by MathTherapy(10557)  (Show Source):
You can put this solution on YOUR website! Keisha drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 8 hours. When Keisha drove home, there was no traffic and the trip only took 6 hours. If her average rate was 16 miles per hour faster on the trip home, how far away does Keisha live from the mountains?
Distance between home and mountains:  miles
You can do the check!!
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