# Math Help - Word Problem - Rational Equation??

1. ## Word Problem - Rational Equation??

Last one - I promise!!

A sludge pool is filled by two inlet pipes. One pipe can fill the pool in 15 days, and the other can fill it in 21 days. However, if nosewage is added, continuous waste removal will empty the pool in 36 days. How long will it take the two inlet pipes to fill an empty sludge pool?

2. Originally Posted by Schoolgirlheart
Last one - I promise!!

A sludge pool is filled by two inlet pipes. One pipe can fill the pool in 15 days, and the other can fill it in 21 days. However, if nosewage is added, continuous waste removal will empty the pool in 36 days. How long will it take the two inlet pipes to fill an empty sludge pool?
What?! The last one?! Anyways:

Pipe 1:

15 days = 1 pool

1 day = $\frac{1}{15}$ portion of the pool

Pipe 2:

21 days = 1 pool

1 day = $\frac{1}{21}$ portion of the pool

So, if you combine pipe 1 and pipe2:

in 1 day they will fill $\frac{1}{15} + \frac{1}{21} = \frac {21+15}{315} = \frac{36}{315} = \frac{4}{35}$ portion of the pool.

so, combined the pipes fill:

$\frac{4}{35}$ portion of the pool= 1 day

the whole pool= $1 \times \frac{35}{4} = 8.75$ days = 8 days and 18 hours

3. Thank you so very much. This board has been very helpful!! Now only if there was a sister board for chemistry..

Thank you!!!

4. Originally Posted by Schoolgirlheart
Thank you so very much. This board has been very helpful!! Now only if there was a sister board for chemistry..

Thank you!!!
Schoolgirlheart'

There is a sister board for chemistry indeed:

http://www.chemistryhelpforum.com/chemistry-help/

5. Well. I'm speechless. Now not only do I have a chemical engineer to tutor me in chemistry, I have you guys!

Thank you!