At their respective rates, pump A, B, and C can fulfill an

Question

At their respective rates, pump A, B, and C can fulfill an empty tank, or pump-out the full tank in 2, 3, and 6 hours. If A and B are used to pump-out water from the half-full tank, while C is used to fill water into the tank, in how many hours, the tank will be empty?

A. 2/3
B. 1
C. 3/4
D. 3/2
E. 2

A. 2/3 
B. 1 
C. 3/4 
D. 3/2 
E. 2

IanStewart · Accepted Answer

You can use a rates formula here, or convert each worker to the same amount of time (6 hours) :

A empties 3 tanks every 6 hours
B empties 2 tanks every 6 hours
 C fills 1 tank every 6 hours 
Together, they empty 4 tanks every 6 hours
So they empty 1 tank every 6/4 hours, and empty half of a tank in 3/4 hours. C.

TGC · Answer

Rate(A)=1/2
Rate(B)=1/3
Rate(C)=1/6

A + B - C

1/2 + 1/3 - 1/6 = 4/6 (Combined rate per the question)

Rate * Time = Work

4/6 * Time = 1/2

Time = 3/4

h2polo · Answer

12.At their respective rates, pump A, B, and C can fulfill an empty tank, or pump-out the full tank in 2, 3, and 6 hours. If A and B are used to pump-out water from the half-full tank, while C is used to fill water into the tank, in how many hours, the tank will be empty?
A. 2/3
B. 1
C. 3/4
D. 3/2
E. 2

let X = # of hours for the tank to empty

X*Rate A + X*Rate B - X*Rate C = 1/2 tank

X*(1/2) + X*(1/3) - X*(1/6) = 1/2
X = 3/4

It takes 3/4 hrs to empty the tank

ANSWER: C. 3/4

crejoc · Answer

that looks so simple and easy.. thanks Ian.

bhanushalinikhil · Answer

Good job Ian. You made it all simple.

age · Answer

Effective rate(empty) : 1/2+1/3-1/6 = 4/6 = 2/3

So whole tank will be emptied in 3/2 hrs..and half will be in 3/4 hrs. C...

rrsnathan · Answer

Hi,

I could understand this method.
But my doubt is
Work = Rate * time
Time = Work / Rate

So as per this problem 
Rate(A)=1/2
Rate(B)=1/3
Rate(C)=1/6

So total time is:
(1/2)/(1/2) + (1/2) / (1/3) - (1/2) / (1/6) = -1/2

Where iam missing something?? Please help me

thanks,
Rrsnathan.

Bunuel · Answer

When adding rates you get combined rate not time. Also, why are you multiplying combined rate by 1/2?

At their respective rates, pump A, B, and C can fulfill an empty tank, or pump-out the full tank in 2, 3, and 6 hours. If A and B are used to pump-out water from the half-full tank, while C is used to fill water into the tank, in how many hours, the tank will be empty? 
A. 2/3 
B. 1 
C. 3/4 
D. 3/2 
E. 2

Rate of A = 1/2 tank/hour;
Rate of B = 1/3 tank/hour;
Rate of C = 1/6 tank/hour.

Combined rate when A and B are used to pump-out water, while C is used to fill water into the tank is 1/2+1/3-1/6=2/3 tank hour.

So, to empty the full tank 3/2 hours (reciprocal of rate) are needed. To empty the half-full tank half of that time would be needed: 1/2*3/2=3/4 hours.

Answer: C.

Hope it's clear.

TooLong150 · Answer

t*  + current tank size = 0
t*  + .5 = 0
t = 3/4

PareshGmat · Answer

Effective rate of A, B & C respectively

= \frac{1}{2} + \frac{1}{3} - \frac{1}{6} 
(-ve as tank is getting empty)

= \frac{3+2-1}{6}

= \frac{4}{6}

= \frac{2}{3}

Time required for full tank  = \frac{3}{2}

Time required for half tank = \frac{3}{2} * \frac{1}{2} = \frac{3}{4}

Answer = C

Rahulnair2802 · Answer

Time required to half the tank by each = (time for full tank)/2
Therefore 
A=1hour
B=3/2 hour
C=6/2 hour
Now A and B empties and C adds
=> 1/A + 1/B - 1/C = 1+2/3-2/6 =8/6=4/3
 hence 3/4 ans

neilsheth1 · Answer

how did the reciprocal come. I mean 2/3 tank per hour into 3/2 I did not get that logic

BrainLab · Answer

Let’s say work = 12 then:
Rate A = 6 
Rate B = 4
Rate C = 2
There combined rate  = 6+4-2=8  and 50% of the tank  =\frac{12}{2}=6 ,  hence 8*t=6, \frac{t=3}{4} 
Answer C

Abhishek009 · Answer

Let the volume of the tank be 12 units

Efficiency of tank A = -6 { -ve since they are pumpung out water}
Efficiency of tank B = -4 { -ve since they are pumpung out water}
Efficiency of tank C = 2

We are given the information that the tank is half filled, so 6 units is filled

Net/Effective work done by the 3 pipes is (-6)+ (-4) +(2) =>-8 units

So, the three pipes will drain out water and the time required to do the same from the half filled tank is 6/8 => 3/4

Answer is (C)

gracie · Answer

t=time to empty tank
t(1/6-5/6)=-1/2➡t(-2/3)=-1/2
t=3/4 hour

sh33pymd · Answer

lets set the equation as:
water in the tank + water pump in = water pump out

This will give you the following:
1/2 + 1/6(T) = (1/2)T + (1/3)T where T is the required time so that the tank is empty
solve for T,
you will get T = 3/4 hr

so the  answer is C

ScottTargetTestPrep · Answer

We can calculate the net outflow rate (i.e., the sum of the rates of A and B minus the rate of C) as:

1/2 + 1/3 - 1/6 = 3/6 + 2/6 - 1/6 = 4/6 = 2/3

Since only ½ of a tank needs to be emptied, the time it takes to do that is (1/2)/(2/3) = 1/2 x 3/2 = 3/4 hour.

Answer: C

GMATinsight · Answer

ANswer: Option C Please check the explanation as attached Screenshot 2020-08-11 at 8.26.25 PM.png

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