SOLUTION: Could you tell me if I have this correct. During rush hour, Bill can drive 15 miles using the side roads in the same time that it takes to travel 10 miles on the freeway. If

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Question 99457: Could you tell me if I have this correct.
During rush hour, Bill can drive 15 miles using the side roads in the same time that it takes to travel 10 miles on the freeway. If Bill's rate on the side roads in 8 mi/h faster than his rate on the freeway, find his rate on the side roads.
Is the answer 24? Thank you.
Answer by ptaylor(2198) (Show Source):
You can put this solution on YOUR website!
I THINK THAT YOU ARE RIGHT ON!!!!!!!!!!!!!!!!
distance(d)=rate(r) times time(t) or d=rt; t=d/r and r=d/t
Let r=his rate on the side roads
Then r-8=his rate on the freeway
Time to drive 15 mi using the side roads=15/r
Time to drive 10 mi using the freeway=10/(r-8)
Now we are told that these two times are the same. So our equation to solve is:
15/r=10/(r-8) multiply both sides by r(r-8)
15(r-8)=10r get rid of parens
15r-120=10r subtract 15r from both sides
15r-15r-120=10r-15r collect like terms
-120=-5r divide both sides by -5
r=24 mph------------------------rate on side roads
CK
15/24=10/16
5/8=5/8
Hope this helps---ptaylor