document.write( "Question 482696: On Jerry's way to work in the morning, he was only able to travel at a rate of 20 mph because of traffic. On his drive home, he averaged 40mph. If his total time was 1 1/2 hours, how long did it take him to drive to work? \n" ); document.write( "

Algebra.Com's Answer #330383 by Alan3354(69443) $\"\"$ $\"About$

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On Jerry's way to work in the morning, he was only able to travel at a rate of 20 mph because of traffic. On his drive home, he averaged 40mph. If his total time was 1 1/2 hours, how long did it take him to drive to work?
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\n" ); document.write( "His average speed for the round trip is
\n" ); document.write( "Avg = 2*20*40/(20 + 40) = 1600/60 = 80/3 mph
\n" ); document.write( "The distance = (80/3) * (3/2) * (1/2) = 20 miles
\n" ); document.write( "His time going was 20/20 = 1 hour
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\n" ); document.write( "Return time = 20/40 = 1/2 hour
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\n" ); document.write( "Not the usual way of working it.
\n" ); document.write( "Here's the proof of the round-trip calculations.
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\n" ); document.write( "r1 = rate going
\n" ); document.write( "r2 = rate returning
\n" ); document.write( "t = d/r1 + d/r2 (total time for round trip of distance 2d)
\n" ); document.write( "t = (d*r1 + d*r2)/(r1*r2) = 2d*(r1 + r2)/r1*r2
\n" ); document.write( "Avg = 2d/t
\n" ); document.write( "--> Avg = 2*r1*r2/(r1 + r2) (similar to parallel resistors or parallel flows, but x2)
\n" ); document.write( "The average speed is less than the average of the 2 speeds (unless they're equal), because more time is spent at the lower speed. \n" ); document.write( "

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