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

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Question 952847: Kevin drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took
8
hours. When Kevin drove home, there was no traffic and the trip only took
6
hours. If his average rate was
16
miles per hour faster on the trip home, how far away does Kevin live from the mountains?

Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
___________________rate____________time__________distance
GOTO________________r________________8___________d
BACK_______________r+16______________6___________d


Variables assigned as understood from data table and description.


Try solving purely in symbols, to solve for d.
Only TWO unknown variables: r and d.


___________________rate____________time__________distance
GOTO________________r________________g___________d
BACK_______________r+k_______________b___________d


Fact for uniform rates for travel, RT=D for rate, time, distance.

system%28rg=d%2C%28r%2Bk%29b=d%29

r%2Bk=d%2Fb
r=d%2Fb-k
-
substitute.
%28d%2Fb-k%29%2Ag=d
%28d-kb%29%2Ag=d%2Ab
dg-kbg=db
dg-db=kbg
d%28g-b%29=kbg
highlight%28d=%28kbg%29%2F%28g-b%29%29

Substitute the values known or given for b, g, k, and evaluate d.