document.write( "Question 766879: Working alone, peter can paint a house in 2h less than Daniel. Working together, they can paint the house in 10h. How long would it take Daniel to paint the house by himself? \n" ); document.write( "
Algebra.Com's Answer #467302 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
Working alone, peter can paint a house in 2h less than Daniel.
\n" ); document.write( " Working together, they can paint the house in 10h.
\n" ); document.write( " How long would it take Daniel to paint the house by himself?
\n" ); document.write( ":
\n" ); document.write( "let d = time required by Daniel alone
\n" ); document.write( "then
\n" ); document.write( "(d-2) = Peter's time alone
\n" ); document.write( ":
\n" ); document.write( "Let the completed job = 1, each will do a fraction of the job, the two fractions add up to 1.
\n" ); document.write( ":
\n" ); document.write( "\"10%2Fd\" + \"10%2F%28%28d-2%29%29\" = 1
\n" ); document.write( "multiply by d(d-2) to clear the denominators, resulting in\"
\n" ); document.write( "10(d-2) + 10d = d(d-2)
\n" ); document.write( "10d - 20 + 10d = d^2 - 2d
\n" ); document.write( "combine as a quadratic equation on the right
\n" ); document.write( "0 = d^2 - 2d - 20d + 20
\n" ); document.write( "d^2 - 22d + 20
\n" ); document.write( "This will not factor, use the quadratic formula to find the reasonable answer
\n" ); document.write( "I got d = 21.05 hrs, Daniels time alone
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check this out using a calc:
\n" ); document.write( "\"10%2F21.05\" + \"10%2F19.05\" ~ 1 \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );