Two taps A and B can fill a water tank in 20 | vedclass

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Question

(NONE) Let the capacity of the tank be $V$ gallons.
The rate of tap $A$ is $\frac{V}{20}$ gallons/min.
The rate of tap $B$ is $\frac{V}{24}$ gallons

Vedclass · Accepted Answer

$120$

Vedclass · Answer

(NONE) Let the capacity of the tank be $V$ gallons.
The rate of tap $A$ is $\frac{V}{20}$ gallons/min.
The rate of tap $B$ is $\frac{V}{24}$ gallons/min.
The rate of tap $C$ is $3$ gallons/min (emptying).
When all three are opened,the net rate is $\frac{V}{15}$ gallons/min.
Therefore,$\frac{V}{20} + \frac{V}{24} - 3 = \frac{V}{15}$.
Rearranging the terms: $\frac{V}{20} + \frac{V}{24} - \frac{V}{15} = 3$.
Taking the $LCM$ of $20, 24,$ and $15$,which is $120$:
$\frac{6V + 5V - 8V}{120} = 3$.
$\frac{3V}{120} = 3$.
$\frac{V}{40} = 3$.
$V = 120 	imes 3 / 3 = 120$ is incorrect based on the previous logic; let's re-calculate: $\frac{3V}{120} = 3 \implies V = 120$.

Two taps $A$ and $B$ can fill a water tank in $20$ $min$ and $24$ $min$ respectively,and a third tap $C$ empties the tank at a rate of $3$ $gallons$ per $min$. If all three taps $A$,$B$,and $C$ are opened together,the tank is filled in $15$ $min$. What is the capacity of the tank in $gallons$?

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