Pipe A can fill a tank in 30 minutes,while pi | vedclass

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Question

(A) Let the total capacity of the tank be the Least Common Multiple $(LCM)$ of $30, 10,$ and $40$,which is $120$ units.Efficiency of pipe $A = 120 / 3

Vedclass · Accepted Answer

$9 \frac{3}{13} 	ext{ minutes}$

Vedclass · Answer

(A) Let the total capacity of the tank be the Least Common Multiple $(LCM)$ of $30, 10,$ and $40$,which is $120$ units.Efficiency of pipe $A = 120 / 30 = 4 	ext{ units/min}$.Efficiency of pipe $B = 120 / 10 = 12 	ext{ units/min}$.Efficiency of pipe $C = 120 / 40 = 3 	ext{ units/min}$ (emptying,so negative).When all pipes are opened together,the net efficiency = $4 + 12 - 3 = 13 	ext{ units/min}$.Time required to fill the tank = $\frac{	ext{Total Capacity}}{	ext{Net Efficiency}} = \frac{120}{13} 	ext{ minutes}$.Converting to mixed fraction: $120 / 13 = 9 \frac{3}{13} 	ext{ minutes}$.

Pipe $A$ can fill a tank in $30$ minutes,while pipe $B$ can fill the same tank in $10$ minutes and pipe $C$ can empty the full tank in $40$ minutes. If all the pipes are opened together,how much time will be needed to make the tank full?

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