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: two-consultants-can-type-up-a-report-126155.html#p1030079

Hope it helps.
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Ans : D

Pipe 1 : Work done in 1 hr = 1/9 = Rate
Pipe 2 : work donr in 1 hr = 1/5 = Rate

Together

Rate * Time = Work
(1/9 + 1/5) * x = 1

x = 45/14
x = 3.21

Select the capacity of the pool as a smart number (9 *5=45 Liters)
For 1st pipe, in 9hours it fills 45 Liters
So in hour, it fills 45/9 = 5

For 2nd pipe, in 5hours it fills 45 Liters
So in hour, it fills 45/5 = 9

So together in 1hour they can fill 9+5=14 Liters

Thus, for 14 Liters time taken = 1 h
For 45 Liters, time taken = (45/14) = 3.2

ANSWER D

Considering the answer choices are not close enough, another quick way to answer this is to work with approximate percentages:

First outlet takes 9 hours to fill the pool, i.e. it fills approx. 11% of the pool every hour. Similarly, second outlet fills 20% of the pool in the same time. Thus, together they will fill approx. 31% of the pool in 1 hour, so to fill 100% of it they will take a little over 3 hours but definitely less than 4 hours. Only choice (D) meets this criteria.

Hope it helps.

Consider tank capacity to be 45l, a smart number divisible by 9 & 5.
First outlet fills the tank in 45/9 = 5 Hrs. (9 liters / Hr.)
Second outlet fills the tank in 45/5 = 9 Hrs. (5 liters / Hr.)
In 1 hour, first and second outlet can fill 9+5 = 14 Liters.
In x hours, first and second outlet can fill 45 Liters.

X = (45*1)/14 = 3.21 Hrs.
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rate of pipe A; 1/9 and pipe B; 1/5
together ; 14/45
time ; 45/14 ; ~ 3.21 ; IMO D
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