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A tank contains G gallons of water. If the water fills the tank at
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22 Dec 2024, 22:35
22 Dec 2024, 22:35
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A tank contains ' $\(G\)$ ' gallons of water. If the water fills the tank at the rate of $\(x\)$ gallons/hour and leaks out of the tank at the rate of y gallons /hour (where, $\(y>x\)$ ), what is the time taken to empty half of the tank (i.e. $\(\frac{G}{2}\)$ gallons) in terms of $x$ and $y$ ?
(A) $\(\frac{G}{y}\)$
(B) $\(\frac{G}{y-x}\)$
(C) $\(\frac{G}{2(y-x)}\)$
(D) $\(\frac{3 G}{4(y-x)}\)$
(E) $\(\frac{G}{y+x}\)$
(A) $\(\frac{G}{y}\)$
(B) $\(\frac{G}{y-x}\)$
(C) $\(\frac{G}{2(y-x)}\)$
(D) $\(\frac{3 G}{4(y-x)}\)$
(E) $\(\frac{G}{y+x}\)$
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A tank contains G gallons of water. If the water fills the tank at
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01 Feb 2025, 11:24
01 Feb 2025, 11:24
Expert Reply
OE
The water in the tank gets filled at the speed of $\(x\)$ gallon/hour and leaks at the rate of $\(y\)$ gallons/hour , so the rate at which the tank gets empty is = Leakage rate - Filling rate $\(=(y-x)\)$ gallons $/$ hour
We know, Time $\(=\frac{Work }{ Speed }\)$, so the time taken to empty half of the tank i.e. $\(\frac{G}{2}\)$ gallons would be
$$
\(\frac{\frac{G}{2}}{(y-x)} \text { sec onds }=\frac{G}{2(y-x)} \)
$$
Hence the answer is (C).
The water in the tank gets filled at the speed of $\(x\)$ gallon/hour and leaks at the rate of $\(y\)$ gallons/hour , so the rate at which the tank gets empty is = Leakage rate - Filling rate $\(=(y-x)\)$ gallons $/$ hour
We know, Time $\(=\frac{Work }{ Speed }\)$, so the time taken to empty half of the tank i.e. $\(\frac{G}{2}\)$ gallons would be
$$
\(\frac{\frac{G}{2}}{(y-x)} \text { sec onds }=\frac{G}{2(y-x)} \)
$$
Hence the answer is (C).
gmatclubot
A tank contains G gallons of water. If the water fills the tank at [#permalink]
01 Feb 2025, 11:24
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