The water from one outlet, flowing at a constant rate, can

Question

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

(A) 0.22 
(B) 0.31 
(C) 2.50 
(D) 3.21 
(E) 4.56

Bunuel · Accepted Answer

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.

shadabkhaniet · Answer

Always remember RT=W i.e Rate*Time = Work

Also remember that rate can be added or subtracted. For e.g if A do a work in 2 day and B do a work in 2 day. 
They both of them together will do a work in 1 day.

So now your question first determine both outlets rate.
1st outlet rate = 1/9 (R=W/T here W=1 work, T = 9hrs) 
2nd outlet rate = 1/5 (R=W/T here W=1 work, T = 5hrs)

Both of them working together rate = 1st outlet rate + 2nd outlet rate = 1/9+1/5 = 14/45

again apply the formula RT=W 
T = W/R = 1/14/45 = 45/14 =3.21

Answer is D.
Hope this helps.

kuttingchai · Answer

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

email2vm · Answer

This really helped in clearing all the queries

djdhiman · Answer

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

EMPOWERgmatRichC · Answer

Hi All,

This question is a standard "Work Formula" question. When you have 2 entities sharing a task, you can use the following formula to figure out how long it takes for the 2 entities to complete the task together.

Work = (A)(B)/(A+B) where A and B are the individual times required to complete the task

Here, we're given the rates as 9 hours and 5 hours. Using the Work Formula, we have...

(9)(5)/(9+5) = 45/14

45/14 is a little more than 3.....there's only one answer that matches...

Final Answer:  D

GMAT assassins aren't born, they're made,
Rich

Dienekes · Answer

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.

JeffTargetTestPrep · Answer

This problem is called a combined work problem. In these problems we use the formula:

Work (of machine 1) + Work (of machine 2) = Total Work Done

In this particular problem we can define “machine” as “outlet”. We are given that the water from one outlet, flowing at a constant rate, can fill a swimming pool in 9 hours and that the water from a second outlet, flowing at a constant rate, can fill the same pool in 5 hours. This means the hourly rate for one outlet is 1/9 pool per hour and the rate of the other outlet is 1/5 pool per hour. We also are told that the two outlets work together to fill the pool. Thus they both work together for “T” hours. We can fill these values into a simple table.

https://i.imgur.com/2b02MKg.png

We can plug in the two work values for outlet one and outlet two into the combined worker formula.

Work (of outlet 1) + Work (of outlet 2) = Total Work Done

T/9 + T/5 = 1

To eliminate the need for working with fractions, let's multiply the entire equation by 45.

45(T/9 + T/5 = 1)

5T + 9T = 45

14T = 45

T = 45/14 = 3 3/14 ≈ 3.21 hours

Answer D

herbgatherer · Answer

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.

BrentGMATPrepNow · Answer

So, let's say that the volume of the pool is  45 gallons .

The water from one outlet, flowing at a constant rate, can fill a swimming pool in 9 hours  
So, this outlet pumps at a rate of   5   gallons per hour

The water from a second outlet, flowing at a constant rate, can fill the same pool in 5 hours.   
So, this outlet pumps at a rate of   9   gallons per hour

If both outlets are used at the same time. . .   
The combined rate of both pumps = (  5   gallons per hour) + (  9   gallons per hour)
=    14   gallons per hour

Time = output/rate 
At   14   gallons per hour, the time to pump  45  gallons =   45 /  14  
= 3 3/14
= 3.something

Answer: D

Cheers,
Brent

Archit3110 · Answer

rate of pipe A; 1/9 and pipe B; 1/5
together ; 14/45
time ; 45/14 ; ~ 3.21 ; IMO D

Hovkial · Answer

OFFICIAL GMAT EXPLANATION

The first outlet can fill the pool at a rate of  1/9  of the pool per hour, and the second can fill the pool at a rate of  1/5  of the pool per hour. Together, they can fill the pool at a rate of  1/9 + 1/5 = 5/45 + 9/45 = 14/45  of the pool per hour. Thus, when both outlets are used at the same time, they fill the pool in  45/14 = 3.21  hours.

The correct answer is D.

ArnauG · Answer

Let's denote the rate of the first outlet as R1 (in units of pool/hour) and the rate of the second outlet as R2.

From the problem, we know that R1 = 1/9 (since it takes 9 hours for one outlet to fill the pool) and R2 = 1/5 (since it takes 5 hours for the other outlet to fill the pool).

When both outlets are used together, their rates add up:

R1 + R2 = 1/9 + 1/5 = 14/45

Therefore, the combined outlets can fill the pool at a rate of 14/45 pool per hour.

To find approximately how many hours it takes to fill the pool using both outlets, we can use the formula:

time = amount of work / rate

Since the amount of work is 1 pool and the combined rate of the outlets is 14/45 pool per hour, we have:

time = 1 / (14/45) = 45/14 ≈ 3.21

Therefore, approximately 3.21 hours are required to fill the pool using both outlets.

The answer is (D) 3.21.

Ratanp · Answer

D, 
in simple steps, if you ever have to find efficieny and both working together just do it this way. 
= 9:5 (common is 45)
 9:5 (multiply bigger with smaller or smaller with bigger and add the second one in ratios together)
= 45/14= 3.21 (D)

totaltestprepNick · Answer

D https://www.youtube.com/watch?v=dRC0I8wEUP4 Nick Slavkovich, GMAT/GRE tutor with 20+ years of experience tutoring@totaltestprep.net

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