Two pipes A and B can fill a cistern in 15 an | vedclass

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Question

(B) Pipe $A$ fills the cistern in $15 	ext{ min}$,so its rate is $\frac{1}{15}$ of the tank per minute.Pipe $B$ fills the cistern in $20 	ext{ min}$

Vedclass · Accepted Answer

$\frac{52}{3} 	ext{ min}$

Vedclass · Answer

(B) Pipe $A$ fills the cistern in $15 	ext{ min}$,so its rate is $\frac{1}{15}$ of the tank per minute.Pipe $B$ fills the cistern in $20 	ext{ min}$,so its rate is $\frac{1}{20}$ of the tank per minute.Both pipes are opened for $2 	ext{ min}$. The work done by both pipes in $2 	ext{ min}$ is $2 	imes (\frac{1}{15} + \frac{1}{20}) = 2 	imes (\frac{4+3}{60}) = 2 	imes \frac{7}{60} = \frac{7}{30}$.Remaining work to be filled by pipe $B$ is $1 - \frac{7}{30} = \frac{23}{30}$.Time taken by pipe $B$ to fill the remaining part is $\frac{23/30}{1/20} = \frac{23}{30} 	imes 20 = \frac{46}{3} 	ext{ min}$.Total time taken = (Time both pipes were open) + (Time pipe $B$ was open alone) = $2 + \frac{46}{3} = \frac{6+46}{3} = \frac{52}{3} 	ext{ min}$.

Two pipes $A$ and $B$ can fill a cistern in $15$ and $20$ $min$,respectively. Both the pipes are opened together,but after $2$ $min$,pipe $A$ is turned off. What is the total time (in $minutes$) required to fill the tank?

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