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  • It can take 12 hours to fill a swimming pool using two pipes. If the pipe of larger diameter is used for four hours and the pipe of smaller diameter for 9 hours, only half of the pool can be filled. How long would it take for each pipe to fill the pool

It can take 12 hours to fill a swimming pool using two pipes. If the pipe of larger diameter is used for four hours and the pipe of smaller diameter for 9 hours, only half of the pool can be filled. How long would it take for each pipe to fill the pool separately ?

 

 
 
 
 
 

Answers (1)

$ Let larger diameter pipe (Pipe P) take x hrs to fill the swimming pool separately $ \\ $ In 1 hour the Pipe P fill = $\frac{1}{x}$ of swimming pool $ \\\\ $ Let smaller diameter pipe (Pipe Q) take y hrs to fill the swimming pool separately $ \\ $ In 1 hour the Pipe Q fill = $\frac{1}{y}$ of swimming pool $ \\\\ $ATQ$ \\ \frac{1}{x}+\frac{1}{y}=\frac{1}{12} ....(i)\\\\ \frac{4}{x}+\frac{9}{y}=\frac{1}{2}...(ii)\\

\\ 4 \times Equation (i) - Equation (i) \\\\ \frac{4}{x}+\frac{4}{y}- \frac{4}{x}-\frac{9}{y}=\frac{1}{3} - \frac{1}{2} \\ \frac{-5}{y } = \frac{-1}{6} \\ y = 30 \ hrs \\ $ Put value of y in quation (i) $\\ \frac{1}{x} + \frac{1}{30} = \frac{1}{12} \\\\ \frac{1}{x} = \frac{5-2}{60} \\\\ x =20 \ hrs \\

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