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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