SOLUTION: Becky can ride her bike to the university library in 20 min. The trip home, which is all uphill takes her 30 min. If her rate is 8mph faster on the way there than the way home, how

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Becky can ride her bike to the university library in 20 min. The trip home, which is all uphill takes her 30 min. If her rate is 8mph faster on the way there than the way home, how      Log On

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Question 416339: Becky can ride her bike to the university library in 20 min. The trip home, which is all uphill takes her 30 min. If her rate is 8mph faster on the way there than the way home, how far does she live from the library?
Found 2 solutions by josmiceli, htmentor:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Equation for downhill:
d+=%28+r%2B+8%29%2A%2820%2F60%29
Uphill:
d+=+r%2A%2830%2F60%29
---------------
This is 2 equations and 2 unknowns, so it's solvable
The d's are the same, so
%28r+%2B+8%29%2A%281%2F3%29+=+%281%2F2%29%2Ar
+%281%2F3%29%2Ar+%2B+8%2F3+=+%281%2F2%29%2Ar+
The LCD is 6
+2r+%2B+16+=+3r
r+=+16 mi/hr
Now find d
d+=+%281%2F2%29%2Ar
d+=+%281%2F2%29%2A16
d+=+8
She lives 8 mi from the library

Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
Let s = her speed on the way to the library in mph
Her speed on the way from the library = s - 8
Her travel times in hours are
20 min/60 min = 1/3 hr (to) and 30/60 = 1/2 hr (from) library
The distance from home to library = s*(1/3)
The distance from library to home = (s-8)*(1/2)
Since these two distances are equal, we have s%2F3+=+%28s-8%29%2F2
Solving for s gives %28-1%2F6%29s+=+-4 -> s = 24 mph
Therefore, the distance to the library = 24 mph*(1/3 hr) = 8 miles