Question

One pipe fills a storage pool in 20 hours, another pipe fills the same pool in 15 hours.
If a third person joins and all together it takes 6hours, how long will it take the third person to fill the pool?

Answer 1

x=time  of the third person it would take to fill the pool 
We can suggest this equation:
6[(1/20) + (1/15) +(1/x)]=1
6[(3x+4x+60)/60x]=1
(7x+60)/10x=1
7x+60=10x
7x-10x=-60
-3x=-60
x=-60/-3
x=20

Answer: the third person alone would fill the pool in 20 hours .

Answer 2

It will take the third person 20 hours to fill the pool.

Let the time it will take the third person to fill the pool be x

If one pipe fills a storage pool in 20 hours, another pipe fills the same pool in 15 hours, both pipes will fill the pool in $\frac{1}{20} +\frac{1}{15}$

The third person will fill the pool $\frac{1}{x}$ time in an hour.

Taking the sum of the time and equating it to 1/6 will give;

$\frac{1}{20} +\frac{1}{15} + \frac{1}{x} = \frac{1}{6}\\\frac{3+4}{60} + \frac{1}{x} = \frac{1}{6}\\\frac{7}{60} + \frac{1}{x} = \frac{1}{6}\\\frac{1}{x} = \frac{1}{6} - \frac{7}{60} \\\frac{1}{x} = \frac{10-7}{60}\\\frac{1}{x} =\frac{3}{60}\\x=\frac{60}{3}\\x= 20 hours$

This shows that it will take the third person 20 hours to fill the pool.

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