Two pipes,A and B, can separately fill a tank | vedclass

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(B) Pipe $A$ fills $\frac{1}{6}$ of the tank in $1$ hour,and pipe $B$ fills $\frac{1}{8}$ of the tank in $1$ hour.Combined work of $A$ and $B$ in $1$

Vedclass · Accepted Answer

$6$

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(B) Pipe $A$ fills $\frac{1}{6}$ of the tank in $1$ hour,and pipe $B$ fills $\frac{1}{8}$ of the tank in $1$ hour.Combined work of $A$ and $B$ in $1$ hour $= \frac{1}{6} + \frac{1}{8} = \frac{4+3}{24} = \frac{7}{24}$.Work done by both pipes in $1 \frac{1}{2}$ hours (or $\frac{3}{2}$ hours) $= \frac{7}{24} 	imes \frac{3}{2} = \frac{7}{16}$.Remaining part of the tank to be filled $= 1 - \frac{7}{16} = \frac{9}{16}$.Since pipe $A$ is turned off,pipe $B$ fills the remaining $\frac{9}{16}$ part.Time taken by pipe $B$ to fill $\frac{9}{16}$ part $= \frac{9/16}{1/8} = \frac{9}{16} 	imes 8 = \frac{9}{2} = 4.5$ hours.Total time taken to fill the tank $= 1.5$ hours (initial) $+ 4.5$ hours (remaining) $= 6$ hours.

Two pipes,$A$ and $B,$ can separately fill a tank in $6$ $hours$ and $8$ $hours,$ respectively. Both the pipes are opened together,but $1 \frac{1}{2}$ $hours$ later pipe $A$ is turned off. How much time (in $hours$) will it take to fill the tank?

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