document.write( "Question 803144: What is the average speed of a cyclist who bikes up a hill at 6mph but then bikes back along the same path down the hill at 12 mph? \n" ); document.write( "

Algebra.Com's Answer #484146 by Alan3354(69443) $\"\"$ $\"About$

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What is the average speed of a cyclist who bikes up a hill at 6mph but then bikes back along the same path down the hill at 12 mph?
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\n" ); document.write( "Avg = 2*6*12/(6+12)
\n" ); document.write( "= 8 mi/hr
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\n" ); document.write( "d = r*t
\n" ); document.write( "----
\n" ); document.write( "r1 = going
\n" ); document.write( "r2 = returning
\n" ); document.write( "---
\n" ); document.write( "t = d/r1 + d/r2 (d = one-way distance)
\n" ); document.write( "t = (d*r1 + d*r2)/(r1*r2)
\n" ); document.write( "t = d*(r1+r2)/(r1*r2)
\n" ); document.write( "For the round-trip:
\n" ); document.write( "t = 2d*(r1+r2)/(r1*r2)
\n" ); document.write( "r for round trip = 2d/t
\n" ); document.write( "t/2d = (r1+r2)/(r1*r2)
\n" ); document.write( "Invert
\n" ); document.write( "2d/t = r1*r2/(r1+r2)
\n" ); document.write( "Using 2d for distance
\n" ); document.write( "avg r = 2r1*r2/(r1+r2)
\n" ); document.write( "-----
\n" ); document.write( "This is similar to parallel resistances and parallel flows, but with a factor of 2 for the round-trip (of trips of equal distance) \n" ); document.write( "

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