calreg11 wrote:
The water from one outlet, flowing at a constant rate, can fill a swimming pool in 9 hours. The water from a second outlet, flowing at a constant rate, can fill the same pool in 5 hours. If both outlets are used at the same time, approximately what is the number of hours required to fill the pool?
A. 0.22
B. 0.31
C. 2.50
D. 3.21
E. 4.56
Remember we can add the rates of individual entities to get the combined rate.
Generally for multiple entities: \(\frac{1}{t_1}+\frac{1}{t_2}+\frac{1}{t_3}+...+\frac{1}{t_n}=\frac{1}{T}\), where \(T\) is time needed for these entities to complete a given job working simultaneously and \(t_1\), \(t_2\), ..., \(t_n\) are individual times needed for them to complete the job alone.
So for two pumps, workers, etc. we'll have \(\frac{1}{t_1}+\frac{1}{t_2}=\frac{1}{T}\) --> \(T=\frac{t_1*t_2}{t_1+t_2}\) (general formula for 2 workers, pumps, ...).
Back to the original problem: for two outlets the formula becomes: \(\frac{1}{9}+\frac{1}{5}=\frac{1}{T}\) --> \(\frac{14}{45}=\frac{1}{T}\) --> \(T=\frac{45}{14}=3.something\) (or directly \(T=\frac{t_1*t_2}{t_1+t_2}=\frac{5*9}{5+9}=\frac{45}{14}\)).
Answer: D.
Alliteratively you can do: if both outlets were as slow as the first one, so if both needed 9 hours, then together they would fill the pool in 9/2=4.5 hours, since we don't have two such slow outlets then
the answer must be less than 4.5. Similarly, if both outlets were as fast as the second one, so if both needed 5 hours, then together they would fill the pool in 5/2=2.5 hours, since we don't have two such fast outlets then
the answer must be more than 2.5. Only answer choice D meets these requirements.
Answer: D.
Check this for more on this subject:
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