Two pipes

How long will the pool be filled with a double supply pipe if it takes the pool to fill the first pipe by 4 hours longer and the second pipe 9 hours longer than both pipes open at the same time?

Result

t =  6 h

Solution:

$t_{ 1 }=t+4 \ \\ t_{ 2 }=t+9 \ \\ \ \\ t \cdot \ (\dfrac{ 1 }{ t_{ 1 } } + \dfrac{ 1 }{ t_{ 2 } } )=1 \ \\ t \cdot \ (\dfrac{ 1 }{ t+4 } + \dfrac{ 1 }{ t+9 } )=1 \ \\ \ \\ t \cdot \ (t+9) + t \cdot \ (t+4)=(t+9) \cdot \ (t+4) \ \\ t^2=36 \ \\ \ \\ t>0 \ \\ \ \\ t=\sqrt{ 36 }=6 \ \text{h}$

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