# Two valves

Water fill the pool by two valves for 11 days. After 7 days the first valve was stopped and the second valve fill pool for 7 days.

How many days took to fill the pool each of the valves individually?

Result

x =  25.67 d
y =  19.25 d

#### Solution:

$x=1/(1/11-1/(7/(1-7/11)))=25.67 \ \text{d}$
$\dfrac{1}{x}+\dfrac{1}{y} = \dfrac{1}{ 11 } \ \\ 7 \cdot \dfrac{1}{y} = 1- \dfrac{ 7}{ 11 } \ \\ \ \\ y = 7 / (1 - 7/11) = 19.25 \ \text{d} \ \\ \ \\ \dfrac{1}{x} = \dfrac{1}{ 11 } - \dfrac{1}{y} \ \\ \dfrac{1}{x} = \dfrac{1}{ 11 } - \dfrac{1}{ 19.25 } \ \\ \dfrac{1}{x} = 0.039 \ \\ x = 25.67 \ d$

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