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.

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.

If only first inlet pipe is running,
In 9 hours, pool can be filled complete.

so, in 1 hour, fraction of pool filled $= \frac{1}{9}$

similarly,

If only second outlet pipe is running,

in 12 hours, pool can be emptied completely.

so, in 1 hour, fraction of pool emptied, $= \frac{1}{12}$

If both pipes are running, fraction of pool filled $= \frac{1}{9}- \frac{1}{12}$

$=\frac{1}{36}$

so, in 1 hour fraction of pool filled (if both pipes are running) $=\frac{1}{36}$

so, pool can be filled in 36 hours if both pipes running.

3. water entering with the speed 1 pool per 9 hour, say 1/9 pool/hour and the water coming out with speed 1/12

So we want to solve
$\left(\frac{1}{9}-\frac{1}{12}\right)x=1$
NOw solve for x!