Answer
Lucy takes 7.1 hours, Jack takes 9.1 hours
Work Step by Step
Jack and Lucy together boil in 4 hours
Jack takes 2 hours longer than Lucy alone
$1/(x+2) + 1/x = 1/4$
$x*(x+2)*(1/(x+2) + 1/x = 1/4)$
$x + (x+2) = 1/4*(x)(x+2)$
$2x+2 = 1/4(x^2+2x)$
$4*(2x+2) = 4*1/4(x^2+2x)$
$8x+8 = x^2+2x$
$8x+8-8x-8 = x^2+2x-8x-8$
$0 = x^2-6x-8$
A graphing calculator showed $x=-1.123$ and $x=7.123$. We are looking for time, so $x\ne-1.123$.
$7.1 + 2= 9.1$
