document.write( "Question 505214: Together Sophie and Clarissa can paint a house in 6 days. It takes Clarissa 5 days less than Sophie to paint the house by herself. How many days does it take Sophie to paint the house by herself? \n" ); document.write( "
Algebra.Com's Answer #339817 by nerdybill(7384)\"\" \"About 
You can put this solution on YOUR website!
Together Sophie and Clarissa can paint a house in 6 days. It takes Clarissa 5 days less than Sophie to paint the house by herself. How many days does it take Sophie to paint the house by herself?
\n" ); document.write( ".
\n" ); document.write( "Let x = time (days) it takes for Sophie to do it alone
\n" ); document.write( "then
\n" ); document.write( "x-5 = time it takes for Clarissa
\n" ); document.write( ".
\n" ); document.write( "6(1/x + 1/(x-5)) = 1
\n" ); document.write( "multiplying both sides by x(x-5):
\n" ); document.write( "6(x-5 + x) = x(x-5)
\n" ); document.write( "6(2x-5) = x(x-5)
\n" ); document.write( "12x-30 = x^2-5x
\n" ); document.write( "-30 = x^2-17x
\n" ); document.write( "0 = x^2-17x+30
\n" ); document.write( "0 = (x-15)(x-2)
\n" ); document.write( "x = {15, 2}
\n" ); document.write( "the 2 won't make sense, throw it out leaving:
\n" ); document.write( "x = 15 days (Sophie's time)
\n" ); document.write( ".
\n" ); document.write( "Clarissa:
\n" ); document.write( "x-5 = 15-5 = 10 days\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );