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21 Dec 2017, 20:46
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B
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Two hoses, Hose X and Hose Y, are used to fill a pool. Working alone, Hose X can fill 1/x of the pool in 15 minutes. What fraction of the pool can Hose Y fill in 15 minutes if, working together, the two hoses can fill the entire pool in one hour?
A. (x−4)/x
B. (x−4)/(4x)
C. (4−x)/x
D. x/(4−x)
E. 4x/(x−4)
A. (x−4)/x
B. (x−4)/(4x)
C. (4−x)/x
D. x/(4−x)
E. 4x/(x−4)
22 Dec 2017, 18:35
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Bunuel
This question has a hitch: different units for work rates (minutes vs. hours)
Rate of X
In 15 minutes, Hose X can fill \(\frac{1}{x}\) of the pool
15 minutes = \(\frac{1}{4}\) hour
So in one hour, Hose X can do 4 times as much work as it can in 15 minutes
\((\frac{1}{x} * 4) = \frac{4}{x}\) = hourly work rate of Hose X
Rate of Y
X and Y can fill one pool in one hour
X's rate + Y's rate = \(\frac{1 pool}{1 hr}\) = \(1\)
\(\frac{4}{x}\) + Y's rate = \(1\)
\((1 - \frac{4}{x})\) = Y's rate
\((1 - \frac{4}{x}) = (\frac{x - 4}{x})\) = hourly work rate of Hose Y
Y fills how much?
At that rate, what fraction of the pool can Y fill in 15 minutes (= \(\frac{1}{4}\) hour)?
(Y's work rate per hour, r) * (\(\frac{1}{4}\) hour t) = (work finished W)
\((\frac{x - 4}{x}) * (\frac{1}{4}) = \frac{(x - 4)}{(4x)}\)
Answer B
General Discussion
21 Dec 2017, 22:43
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Bunuel
The answer is E
Hose X can fill 1/x in 15 minutes , then it will fill the tank in 15x minutes
Similarly let us suppose that the fill rate of hose Y is y in 15 minutes then to fill full tank it will take 15y
Setting up the equation we have =1/15x+1/15y=1/60
solving we get 4x/(x-4)
