# Math Help - Math 102 - Word Problem

1. ## Math 102 - Word Problem

I need help. I suck at doing Math.

Here it goes...

An inlet pipe can fill a swimming pool in 9hrs and an outlet pipe can empty the pool in 12hrs. Through an error, both pipes are left open. How long will it take to fill the pool?

(Algebraic solutions only!)

I tried to set it up, but I'm not sure if I did it right, and my answer was 9hrs.

9/x = 12/x+3
LCD = x(x+3)
9x+27=12x
27=3x
x=9

It seems too easy. I'm doing it wrong, I can feel it.

2. the inlet pipe by itself (no drainage) takes 9 hrs to fill the pool. that alone should tell you something about your solution.

inlet pipe rate of fill ... $\frac{1 \, \, pool}{9 \, \, hrs}$

outlet pool drain rate ... $\frac{1 \, \, pool}{12 \, \, hrs}$

$\left(\frac{1 \, \, pool}{9 \, \, hrs} - \frac{1 \, \, pool}{12 \, \, hrs}\right) \cdot (t \, \, hrs) = 1 \, \, pool \, \, filled$

$\left( \frac{1}{9} - \frac{1}{12} \right) t = 1$

$\left( \frac{4}{36} - \frac{3}{36} \right) t = 1$

$\frac{t}{36} = 1$

$t = 36 \, \, hrs$

3. You're my herooooooo!