Two pipes A and B can fill a water tank in 10 | vedclass

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(C) Let the capacity of the tank be $V$ gallons.Rate of pipe $A = \frac{V}{10}$ gallons/min.Rate of pipe $B = \frac{V}{12}$ gallons/min.Rate of pipe $

Vedclass · Accepted Answer

$45$

Vedclass · Answer

(C) Let the capacity of the tank be $V$ gallons.Rate of pipe $A = \frac{V}{10}$ gallons/min.Rate of pipe $B = \frac{V}{12}$ gallons/min.Rate of pipe $C = -6$ gallons/min (since it empties the tank).When $A, B,$ and $C$ are opened together,the net rate is $\frac{V}{20}$ gallons/min.Therefore,the equation is: $\frac{V}{10} + \frac{V}{12} - 6 = \frac{V}{20}$.Rearranging the terms: $\frac{V}{10} + \frac{V}{12} - \frac{V}{20} = 6$.Taking the least common multiple $(LCM)$ of $10, 12,$ and $20$,which is $60$:$\frac{6V + 5V - 3V}{60} = 6$.$\frac{8V}{60} = 6$.$\frac{2V}{15} = 6$.$V = \frac{6 	imes 15}{2} = 45$ gallons.Thus,the capacity of the tank is $45$ gallons.

Two pipes $A$ and $B$ can fill a water tank in $10$ and $12$ $min,$ respectively,and a third pipe $C$ can empty it at the rate of $6$ $gallons$ per $min.$ If $A, B,$ and $C$ are opened together,they fill the tank in $20$ $min.$ What is the capacity (in $gallons$) of the tank?

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