Three pumps

We are filling the pool. The first pump would be filled in 12 hours, the second pump in 15 hours. If all three pumps were running at the same time, it would fill the pool for 4 hours. How long would the pool fill only with the third pump?

Result

x =  10 h

Solution:

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

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