document.write( "Question 254913: A man ran 8 miles and walked 6 miles. if he ran 5 mph faster than he walked, and the total time was 2 hours, how fast did he walk? \n" ); document.write( "

Algebra.Com's Answer #187259 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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A man ran 8 miles and walked 6 miles. If he ran 5 mph faster than he walked,
\n" ); document.write( " and the total time was 2 hours, how fast did he walk?
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\n" ); document.write( "Let s = his walking speed
\n" ); document.write( "then
\n" ); document.write( "(s+5) = his running speed
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\n" ); document.write( "Write a time equation, Time = dist/speed
\n" ); document.write( "Running time + walking time = 2 hrs
\n" ); document.write( " $\"8%2F%28s%2B5%29\"$ + $\"6%2Fs\"$ = 2
\n" ); document.write( "Multiply equation by s(s+5), results:
\n" ); document.write( "8s + 6(s+5) = 2s(s+5)
\n" ); document.write( ":
\n" ); document.write( "8s + 6s + 30 = 2s^2 + 10s
\n" ); document.write( ":
\n" ); document.write( "14s + 30 = 2s^2 + 10s
\n" ); document.write( "Arrange as a quadratic equation
\n" ); document.write( "2s^2 + 10s - 14s - 30 = 0
\n" ); document.write( ":
\n" ); document.write( "2s^2 - 4s - 30 = 0
\n" ); document.write( "simplify, divide by 2
\n" ); document.write( "s^2 - 2s - 15 = 0
\n" ); document.write( "Factor
\n" ); document.write( "(s-5)(s+3) = 0
\n" ); document.write( "The positive solution is what we want here
\n" ); document.write( "s = 5 mph, walking speed
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\n" ); document.write( ":
\n" ); document.write( "Check solution
\n" ); document.write( "8/10 + 6/5 =
\n" ); document.write( ".8 + 1.2 = 2 hrs
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