Three pumps

We are filling the pool. The pool would fill the first pump in 12 hours and the second in 15 hours. If all three pumps ran simultaneously, they would fill the pool for 4 hours. How long would the pool fill only with the third pump?

Correct answer:

x =  10 h

Step-by-step explanation:

$$\begin{gathered} 4\cdot (\frac{1}{12}+\frac{1}{15}+\frac{1}{x})=1 \\ 4\cdot (x/12+x/15+1)=x \\ 24x=240 \\ x=\frac{240}{24}=10 \\ x=10=10\text{h} \end{gathered}$$

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