document.write( "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? \n" ); document.write( "

Algebra.Com's Answer #291700 by htmentor(1343) $\"\"$ $\"About$

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Let s = her speed on the way to the library in mph
\n" ); document.write( "Her speed on the way from the library = s - 8
\n" ); document.write( "Her travel times in hours are
\n" ); document.write( "20 min/60 min = 1/3 hr (to) and 30/60 = 1/2 hr (from) library
\n" ); document.write( "The distance from home to library = s*(1/3)
\n" ); document.write( "The distance from library to home = (s-8)*(1/2)
\n" ); document.write( "Since these two distances are equal, we have $\"s%2F3+=+%28s-8%29%2F2\"$
\n" ); document.write( "Solving for s gives $\"%28-1%2F6%29s+=+-4\"$ -> s = 24 mph
\n" ); document.write( "Therefore, the distance to the library = 24 mph*(1/3 hr) = 8 miles \n" ); document.write( "

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