# A small pipe takes 24 minutes longer to fill a tank than it takes a large pipe. The two pipes together can fill the tank in 9 minutes. How long does it take each pipe alone to fill the tank?

Oct 13, 2015

I found $36 \min$ for the small and $12 \min$ for the large

#### Explanation:

Call $s$ the carryng capacity in liters/minute of the small pipe and $l$ of the large. You can write:
$s = \frac{x}{t}$
$l = \frac{x}{t - 24}$
$s + l = \frac{x}{9}$ where $x$ is the capacity of the tank in liters.
Substituting the first 2 into the last:
$\frac{x}{t} + \frac{x}{t - 24} = \frac{x}{9}$ cancel the $x$s:
$\frac{1}{t} + \frac{1}{t - 24} = \frac{1}{9}$
$\left(t - 24 + t\right) 9 = t \left(t - 24\right)$
$18 t - 216 = {t}^{2} - 24 t$
${t}^{2} - 42 t + 216 = 0$
${t}_{1} = 6 \min$ NO too small
${t}_{2} = 36 \min$ YES