Answer
5.2 hours for large pipe, 7.2 hours for small pipe
Work Step by Step
large pipe and small pipe can fill in 3 hours
large pipe can fill in $1/(x-2)$ hours, small pipe can fill in $1/x$ hours
$1/(x-2) + 1/x = 1/3$
$3*x*(x-2)*(1/(x-2) + 1/x = 1/3)$
$3x + 3(x-2) = x(x-2)$
$3x +3x-6 = x^2-2x$
$6x-6=x^2-2x$
$6x-6-6x+6=x^2-2x-6x+6$
$0 = x^2-8x+6$
A graphing calculator showed $x=.838$ and $x=7.162$. However, $x\ne.838$ since the large pipe would have a negative time.
$x=7.2$ hours
$7.2-2=5.2$
