document.write( "Question 508414: A roofer and his assistant working together can finish a roofing job in 4 hours. The roofer working alone could finish the job in 6 hours less than the assistant working alone. How long would it take the roofer working alone?\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #340992 by nerdybill(7384)\"\" \"About 
You can put this solution on YOUR website!
A roofer and his assistant working together can finish a roofing job in 4 hours. The roofer working alone could finish the job in 6 hours less than the assistant working alone. How long would it take the roofer working alone?
\n" ); document.write( ".
\n" ); document.write( "Let x = time (hours) for assistant alone
\n" ); document.write( "then
\n" ); document.write( "x-6 = time (hours) for roofer
\n" ); document.write( ".
\n" ); document.write( "4(1/x + 1/(x-6)) = 1
\n" ); document.write( "multiplying both sides by x(x-6):
\n" ); document.write( "4((x-6) + x) = x(x-6)
\n" ); document.write( "4(2x-6) = x^2-6x
\n" ); document.write( "8x-24 = x^2-6x
\n" ); document.write( "-24 = x^2-14x
\n" ); document.write( "0 = x^2-14x+24
\n" ); document.write( "0 = (x-2)(x-12)
\n" ); document.write( "x = {2,12}
\n" ); document.write( "we can throw out the 2 (extraneous) leaving:
\n" ); document.write( "x = 12 hours (assistant)
\n" ); document.write( ".
\n" ); document.write( "Roofer working alone:
\n" ); document.write( "x-6 = 12-6 = 6 hours\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );