SOLUTION: Word problems are so confusing....please help. 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.

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Question 110216: Word problems are so confusing....please help.
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 is 8 mi/h faster that his rate on the freeway, find his rate on the side roads.
Thank you.
Found 2 solutions by josmiceli, scott8148:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
There are 2 really powerful tools for these realted rate problems:
1) Set up d+=+r%2At for each trip in the problem and make sure
that your number of unknowns is the same as your number of equations
2) Find the COMMON term in the problem. In this case, it is time, t.
In other problems, it might be d, or r.
r%5Bs%5D = rate on sideroads
t%5Bs%5D = time on sideroads
r%5Bf%5D = rate on freeway
t%5Bf%5D = time on freeway
d+=+r%2At
15+=+r%5Bs%5D%2At%5Bs%5D
10+=+r%5Bf%5D%2At%5Bf%5D these are both given
The times for both trips is the same
t%5Bs%5D+=+t%5Bf%5D this is also given, so I'll just use t for both
r%5Bs%5D+=+r%5Bf%5D+%2B+8 this is given
What do I have so far?
15+=+%28r%5Bf%5D+%2B+8%29%2At
10+=+r%5Bf%5D%2At
sove each for t
t+=+15+%2F+%28r%5Bf%5D+%2B8%29
t+=+10+%2F+r%5Bf%5D
Now set the right sides equal to eachother
15+%2F+%28r%5Bf%5D+%2B8%29+=+10+%2F+r%5Bf%5D
Solve for r%5Bf%5D
10%28r%5Bf%5D+%2B+8%29+=+15%2Ar%5Bf%5D
10%2Ar%5Bf%5D+%2B+80+=+15%2Ar%5Bf%5D
5%2Ar%5Bf%5D+=+80
r%5Bf%5D+=+16mi/hr
But the problem wants r%5Bs%5D
r%5Bs%5D+=+r%5Bf%5D+%2B+8
r%5Bs%5D+=+16+%2B+8
r%5Bs%5D+=+24mph answer
check these by going back to original equations
15+=+r%5Bs%5D%2At
10+=+r%5Bf%5D%2At
-----------------
15+=+24t
10+=+16t
solve each for t -they should be the same
t+=+15%2F24
t+=+10%2F16
They are equal- both are 30/48

Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
Bill's rate on the freeway is 2/3 (10/15) times his rate on the side roads

let x="side road rate" ... (2/3)x=x-8 ... 2x=3x-24