Answer
hose takes 16.5 hours, inlet pipe takes 15.5 hours
Work Step by Step
inlet and hose can fill in 8 hours
inlet alone can fill in 1 hour less than the hose alone
inlet can fill $1/(x-1)$ in an hour, the hose can fill $1/x$ in an hour
$1/x + 1/(x-1) = 1/8$
$x*(x-1)*(1/x + 1/(x-1) = 1/8)$
$1(x-1) + x = x*(x-1)/8$
$x-1 + x = (x^2-x)/8$
$2x-1 = (x^2-x)/8$
$8*(2x-1) = 8*(x^2-x)/8$
$16x-8 = x^2-x$
$16x-8-16x+8 =x^2-x-16x+8$
$0 = x^2-17x+8$
A graphing calculator showed $x=.484$ and $x=16.51$. However, $x\ne.484$ since we have to decrease the time by an hour.
$16.51-1=15.51$
