document.write( "Question 308472: Colleen can paint a house in 2 hours less than james. Working together they can paint the house in 10 hours. How long would it take james to pain the house by himself? \n" ); document.write( "

Algebra.Com's Answer #220639 by mananth(16946) $\"\"$ $\"About$

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Colleen can paint a house in 2 hours less than james. Working together they can paint the house in 10 hours. How long would it take james to pain the house by himself?\r
\n" ); document.write( "\n" ); document.write( "let james take x hours to paint the house.
\n" ); document.write( "He will paint 1/x of the house in 1 hour.
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\n" ); document.write( "Colleen takes x-2 hours to do the same job
\n" ); document.write( "she will paint 1/ x-2 of the job in 1 hour
\n" ); document.write( "..
\n" ); document.write( "They both can do the same job in 10 hours
\n" ); document.write( "they do 1/10 of the job in 1 hour
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\n" ); document.write( "1/x + 1/ x-2 = 1/10\r
\n" ); document.write( "\n" ); document.write( "add the fractions: LCM = x(x-2)
\n" ); document.write( "x-2 + x / x(x-2) = 1/10
\n" ); document.write( "2x-2 = x(x-2) /10
\n" ); document.write( "10(2x-2) = x(x-2)
\n" ); document.write( "20x-40= x^2-2x\r
\n" ); document.write( "\n" ); document.write( "x^2-22x+40=0
\n" ); document.write( "x^2 -20x-2x+40=0
\n" ); document.write( "x(x-20)-2(x-20)=0
\n" ); document.write( "(x-20)(x-2)=0
\n" ); document.write( "x= 20 OR 2 hours
\n" ); document.write( "So James can paint the house alone in 20 hours\r
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