Tributaries

The pool can be filled with two different tributaries. The first inflow would fill the pool in 18 hours, both in 6 hours. How many hours would the pool filled with a second inflow?

Result

x =  9 h

Solution:

$6 \cdot \ (1/18 + 1/x)=1 \ \\ y=1/x \ \\ \ \\ 6 \cdot \ (1/18 + y)=1 \ \\ \ \\ 108y=12 \ \\ \ \\ y=\dfrac{ 1 }{ 9 } \doteq 0.111111 \ \\ \ \\ x=1/y=1/0.1111=9 \ \text{h}$

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