Answer
8.5 hours
Work Step by Step
Bill and Billy can clean in 4 hours
Bill takes an hour less than Billy
Let $x$ be how long it takes Bill to clean by himself
$1/x + 1/(x+1) = 1/4$
$4x*(1/x + 1/(x+1) = 1/4)$
$4+(4x/(x+1)) = x$
$(x+1)*(4+(4x/(x+1))) = (x)(x+1)$
$(x+1)*4 + 4x = x^2+x$
$4x+4+4x=x^2+x$
$8x+4 = x^2+x$
$8x+4-8x-4 = x^2+x-8x-4$
$0 = x^2-7x-4$
A graphing calculator shows $x=-.531$ and $x=7.531$. We ignore the $x=-.531$ since we are talking about time.
$7.531 + 1=8.531$
