A water tank is frac{2}{5} full. Pipe A can f | vedclass

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(B) Let the capacity of the tank be $1$ unit.Pipe $A$ fills the tank in $10$ minutes,so its rate is $\frac{1}{10}$ unit/minute.Pipe $B$ empties the ta

Vedclass · Accepted Answer

$6 	ext{ minutes to empty}$

Vedclass · Answer

(B) Let the capacity of the tank be $1$ unit.Pipe $A$ fills the tank in $10$ minutes,so its rate is $\frac{1}{10}$ unit/minute.Pipe $B$ empties the tank in $6$ minutes,so its rate is $-\frac{1}{6}$ unit/minute.When both pipes are open,the net rate is $\frac{1}{10} - \frac{1}{6} = \frac{3-5}{30} = -\frac{2}{30} = -\frac{1}{15}$ unit/minute.The negative sign indicates that the tank is being emptied.The tank is currently $\frac{2}{5}$ full.Time taken to empty the $\frac{2}{5}$ portion = $\frac{	ext{Volume to be emptied}}{	ext{Net rate}} = \frac{2/5}{1/15} = \frac{2}{5} 	imes 15 = 6$ minutes.Therefore,it will take $6$ minutes to empty the tank.

$A$ water tank is $\frac{2}{5}$ full. Pipe $A$ can fill the tank in $10$ $minutes$ and pipe $B$ can empty it in $6$ $minutes$. If both the pipes are open,then how long will it take to empty or fill the tank completely?

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