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?

Correct answer:

t =  6 h

Step-by-step explanation:

$$\begin{gathered} t_1=t+4 \\ {t}_2=t+9 \\ t\cdot ({\displaystyle \frac{1}{t_1}}+{\displaystyle \frac{1}{t_2}})=1 \\ t\cdot ({\displaystyle \frac{1}{t+4}}+{\displaystyle \frac{1}{t+9}})=1 \\ t\cdot (t+9)+t\cdot (t+4)=(t+9)\cdot (t+4) \\ {t}^2=36 \\ t>0 \\ t=\sqrt{36}=6\text{ h} \end{gathered}$$

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