Answer
inlet pipe: 15.5 hours
hose: 16.5 hours
Work Step by Step
inlet pipe: x-1 hours
hose: x hours
$1/x + 1/(x-1) = 1/8$
$1*x*(x-1)*8/x + 1*x*(x-1)*8/(x-1) = 1*x*(x-1)*8/8$
$8x-8+8x=x^2-x$
$16x-8=x^2-x$
$x^2-17x+8=0$
$x=(-b±\sqrt{b^2-4ac})/2a$
$x=(-(-17)±\sqrt{(-17)^2-4*1*8})/2*1$
$x=(17±\sqrt{289-32})/2$
$x=(17±\sqrt{257})/2$
We want a positive value since we are talking about time.
$x=(17±\sqrt{257})/2$
$x=(17+\sqrt{257})/2$
$x=(17+16.03)/2$
$x=33.03/2$
$x=16.515$
inlet pipe: $16.515-1$
$15.515$
