document.write( "Question 214124: It's 56 miles to work, it takes 10 minutes longer to get to work than coming home, and you travel 8 mph faster coming home. What is your avg. speed coming home? \n" ); document.write( "

Algebra.Com's Answer #161737 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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It's 56 miles to work, it takes 10 minutes longer to get to work than coming home,
\n" ); document.write( "and you travel 8 mph faster coming home.
\n" ); document.write( "What is your avg. speed coming home?
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\n" ); document.write( "Let s = speed coming home
\n" ); document.write( "then
\n" ); document.write( "(s-8) = speed going to work
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\n" ); document.write( "Convert 10 min to $\"1%2F6\"$ hr
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\n" ); document.write( "Write a time equation: Time = dist/speed
\n" ); document.write( ":
\n" ); document.write( "Time from work + 10 min = time to work
\n" ); document.write( " $\"56%2Fs\"$ + $\"1%2F6\"$ = $\"56%2F%28%28s-8%29%29\"$
\n" ); document.write( "Multiply equation by 6s(s-8), results:
\n" ); document.write( "56*6*(s-8) + s(s-8) = 6s*56
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\n" ); document.write( "336(s-8) + s^2 - 8s = 336s
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\n" ); document.write( "336s - 2688 + s^2 - 8s - 336s = 0
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\n" ); document.write( "Arrange as a quadratic equation
\n" ); document.write( "s^2 - 8s - 2688 = 0
\n" ); document.write( "Factor to
\n" ); document.write( "(s-56)(s+48) = 0
\n" ); document.write( "positive solution
\n" ); document.write( "s = 56 mph on the return home
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\n" ); document.write( "Check solution (speed to work = 48 mph)
\n" ); document.write( "56/56 + 1/6 = 56/48
\n" ); document.write( "1 + .167 = 1.167 \n" ); document.write( "

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