Pumping alone at their respective constant rates, one inlet pipe fills

Question

Pumping alone at their respective constant rates, one inlet pipe fills an empty tank to 1/2 of capacity in 3 hours and a second inlet pipe fills the same empty tank to 2/3 of capacity in 6 hours. How many hours will it take both pipes, pumping simultaneously at their respective constant rates, to fill the empty tank to capacity?

(A) 3.25
(B) 3.6
(C) 4.2
(D) 4.4
(E) 5.5

Kudos for a correct solution.

A. 3.25
B. 3.6
C. 4.2
D. 4.4
E. 5.5

Abhishek009 · Accepted Answer

Time required to fill the full tank is 6 hours
 
Time required to fill the full tank is 9 hours
 
Use the formula -  \frac{AB}{(A + B)}

Or,  \frac{6*9}{(6 + 9)}

Or,  \frac{54}{15}

Or,  \frac{18}{5}

Or,  3.6

Hence answer is (B) 3.6

cubicleboundmisfit · Answer

1/2 of capacity in 3 hours

full capacity in 6 hours

---> pump A.

2/3 capacity in 6 hours

(2/3 +1/3) in 6+3 = 9 hours

---> pump B

in 1 hour filled 1/6 +1/9 = 5/18 parts 
full in 18/5 hours 3.6 hrs.

HTH

vaibhavtripathi · Answer

Inlet 1 fills x/6 in 1 hour
inlet 2 fills (2x/3)/6 = x/9 in 1 hour

so together in 1 hour they will fill x/6 + x/9 = 5x/18
which means to fill 5x/18 it takes 1 hour => to fill x it will take 18/5=3.6 hrs

CounterSniper · Answer

pipe 1 = 1/6 an hour
pipe 2 = 1/9 an hour

Total time taken =1/6 + 1/9 =3.6 Hours

m2k · Answer

Tank A does 1/2 in 3 hrs so we can fine for full capacity it would take 6 hrs.
Similarly , Tank B takes 2/3rd of tank to be filled in 6 hrs so it would fill to full capacity in 6/(2/3) =>18/2 => 9

Now simple work problem states that it would fill the whole tank in :

1/9 + 1/6 = 5/18 unit =>18/5 hrs = 3.6 hrs

Hence Option B

M3sSiaH · Answer

Total capacity = C

Rate of 1 = C/6
Rate of 2 = C/9 
Combined rate = 5C/18 
Time = 18/5 = 3.6 (B)

GMATinsight · Answer

Time taken by First tank Fill 1/2 the tank = 3 hours
i.e. Time taken by First tank to Fill 1 complete the tank = 6 hours

Time taken by Second tank Fill 2/3 the tank = 6 hours
i.e. Time taken by First tank to Fill 1 complete the tank = (3/2)*6 = 9 hours

in 1 Hour, Both tanks together Fill the tank = (1/6)+(1/9) = 5/18 tank
i.e. Time taken by Both tank to Fill 1 complete the tank = 18/5 hours = 3.6 hours

Answer: option B

TeamGMATIFY · Answer

Assume the volume of the container to be 6 Lts
We have assumed 6 because 6 is the LCM of 2 and 3, the denominators of the capacity filled.

Inlet 1: 1/2 of capacity in 3 hours i.e. 3 lts in 3 hours
Hence 1 lts/hour

Inlet 2: 2/3 of capacity in 6 hours i.e. 4 lts in 6 hours
Hence 2/3 lts/hour

Inlet 1 + Inlet 2 combined rate = 6/(1 + 2/3) hours= 6/ (5/3) hours = 18/5 = 3.6 hours
Option B

NoHalfMeasures · Answer

let c be tank capacity.
Time taken by First pipe to fill 1/2 the tank = 3 hours. So work done in 1 hr= c*{1/(2*3)}= c/6

Time taken by Second pipe to Fill 2/3 the tank = 6 hours. So work done in 1hr= c*{2/(3*6)}=c/9

in 1 Hour, Both tanks together Fill the tank = (1c/6)+(c1/9) = 5c/18 
i.e. Time taken by Both tank to Fill 1 complete the tank = 18/5 hours = 3.6 hours

Answer: option B

shakticnb · Answer

Time taken by First tank Fill 1/2 the tank = 3 hours
i.e. Time taken by First tank to Fill 1 complete the tank = 6 hours

Time taken by Second tank Fill 2/3 the tank = 6 hours
i.e. Time taken by First tank to Fill 1 complete the tank = (3/2)*6 = 9 hours

in 1 Hour, Both tanks together Fill the tank = (1/6)+(1/9) = 5/18 tank
i.e. Time taken by Both tank to Fill 1 complete the tank = 18/5 hours = 3.6 hours

correct answer .... b

mcelroytutoring · Answer

Attached is a visual that should help.

EMPOWERgmatRichC · Answer

Hi All,

This question can be solved in a couple of different ways, but it's essentially just a Work Formula question.

Work = (A)(B)/(A+B) where A and B are the respective times it takes for two entities to individually complete a task.

To start, we have to figure out how long it takes each pipe to fill the FULL tank....

First pipe = fills 1/2 the tank in 3 hours... so it fills the FULL tank in 6 hours 
Second pipe = fills 2/3 the tank in 6 hours... so it fills the FULL tank in 9 hours

Working together, the two pipes will fill the tank in (6)(9)/(6+9) = 54/15 = 3 9/15 hours = 3.6 hours

Final Answer:  B

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

Shiv2016 · Answer

Rate= Work/Time

Let total work = x
 Inlet pipe 1

Time= 3 hours
Work done= 1/2 *x

Rate= x/2/3= x/6

Inlet pipe 2

Time= 6 hours
Work done= 2/3 of x

Rate= 2x/3/6 = x/9

Combined rate=x/6 + x/9= 5x/18

Again the same formula:

Rate= Work/Time
5x/18= x/Time
Time= x/5x/18= 18/5= 3.6

Another method is to consider the total work as the LCM (2,3) (Denominators)

Total work= 6

Inlet pipe 1
Time= 3
Work done= 1/2 *6= 3

Rate= 3/3= 1

Inlet pipe 2
Time= 6
Work done= 2/3 * 6= 4
Rate= 4/6= 2/3

Combined rate= 1+2/3= 5/3

Work= 6

Time= 6/5/3= 18/5= 3.6

ScottTargetTestPrep · Answer

The rate for the first inlet pipe is (1/2)/3 = 1/6 and the rate for the second pipe is (2/3)/6 = 2/18 = 1/9.

If we let t = the number of hours they work together to fill the empty tank, we have:

(1/6)t + (1/9)t = 1

t/6 + t/9 = 1

Multiplying the entire equation by 18, we have:

3t + 2t = 18

5t = 18

t = 18/5 = 3 ⅗ = 3.6

Answer: B

mcelroytutoring · Answer

I have a rather random question for  dabral  and  Bunuel : why can't we use the harmonic mean (average of rates) formula here? Is it sheer coincidence that the answer I am getting (3.75) with this equation is so close to the actual answer (3.6)?

1st pipe rate = 1/6 tank per hour

2nd pipe rate = 1/9 tank per hour

Harmonic mean (average of rates) = #/sum of inverse of rates = 2 / (6 + 9) = (2/15) x 2 = 4/15 per hour. (4/15)x = 1, x = 15/4 = 3.75

Yet the answer is 3.6 with the more traditional (and admittedly easy and straightforward) method. Still, what am I doing wrong? Thanks!

JeffTargetTestPrep · Answer

We are given that the first inlet pipe fills an empty tank to 1/2 capacity in 3 hours. Since rate = work/time, the rate of the first inlet pipe is (1/2)/3 = 1/6.

We are also given that the second inlet pipe fills the same empty tank to 2/3 capacity in 6 hours. Thus, the rate of the second inlet pipe is (2/3)/6 = 1/9.

We need to determine how many hours it will take both pipes, pumping simultaneously at their respective constant rates, to fill the empty tank to capacity.

If we let t = the time in hours the two inlet pipes are working together, then the work of the first inlet pipe = (1/6)t and the work of the second inlet pipe = (1/9)t.

Since the tank is filled, we can set total work to 1 and create the following equation:

(1/6)t + (1/9)t = 1

Multiplying the entire equation by 18, we obtain:

3t + 2t = 18

5t = 18

t = 18/5 = 3.6

Answer: B

BrentGMATPrepNow · Answer

Let's assign a  nice value  to the volume of the tank. We want a volume that works well with the given information (1/2, 2/3, 3 hours and 6 hours).
So, let's say the tank has a total volume of  18  gallons

One inlet pipe fills an empty tank to 1/2 of capacity in 3 hours  
1/2 the tank is 9 gallons. 
So, this pipe fills 9 gallons in 3 hours. 
So, the RATE of this pipe =  3 gallons per hour

A second inlet pipe fills the same empty tank to 2/3 of capacity in 6 hours  
2/3 the tank is 12 gallons. 
So, this pipe fills 12 gallons in 6 hours. 
So, the RATE of this pipe =  2 gallons per hour

So, the  COMBINED  rate of BOTH pumps =  3 gallons per hour  +  2 gallons per hour  =   5 gallons per hour

How many hours will it take both pipes, pumping simultaneously at their respective constant rates, to fill the empty tank to capacity?   
We need to pump  18  gallons of water, and the combined rate is   5 gallons per hour  
Time = output/rate
=  18 /  5  
= 3.6 hours

Answer: B

Cheers.
Brent

Shubhi09 · Answer

1/2 of capacity in 3 hours

full capacity in 6 hours

---> pump A.

2/3 capacity in 6 hours

(2/3 +1/3) in 6+3 = 9 hours

---> pump B

in 1 hour filled 1/6 +1/9 = 5/18 parts 
full in 18/5 hours 3.6 hrs.

Posted from my mobile device

NishantR · Answer

Again a longer solution

What we know
> Tank size is the same hence Tank Size is = 1

Part 1.
>Inflow one takes 3 hrs to fill half 
> hence it takes the 6 hrs to fill the tank 
> hence it fills @ 1/6 per hour

Part 2
> inflow takes 6 hrs to fill 2/3
> hence the remaining 1/3 will take 3 hrs
> hence 6+3= 9 hrs to fill 100%
> hence it fils @ 1/9 per hour

We solve
(1/9)x + (1/6)x = 1
18*(1/9)x + 18(1/6)x = 1*18
2x+3x = 18
5x = 18 
x =18/5
x = 3.6

Pumping alone at their respective constant rates, one inlet pipe fills

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Pumping alone at their respective constant rates, one inlet pipe fills

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