How many hours to fill this water tank?
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- theCodeToGMAT
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Small Pump, A = 2 hrs
Larger Pump, B = 1/2 hr
Total Time = A * B / (A+B ) = 2 * 1/2 / (1/2 + 2) ==> 1 / (5/2) ==> 2/5
Answer [spoiler]{C}[/spoiler]
Larger Pump, B = 1/2 hr
Total Time = A * B / (A+B ) = 2 * 1/2 / (1/2 + 2) ==> 1 / (5/2) ==> 2/5
Answer [spoiler]{C}[/spoiler]
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Hi Yumi2012,
This question is a great example of a "Work Formula" question. Any time you have a question with two entities (people, machines, etc.) who can each do a particular job alone at a set rate, but work together - then you're dealing with the Work Formula.
The Work Formula: [AxB]/[A+B]
Just plug in the two times (in this case, 2 hours and 1/2 hour) in for A and B and you'll have the time it would take the two working together to finish the job.
Rahul's answer shows the math and the correct answer.
You'll likely see this concept once on Test Day (and it might be more complex than this question), so be on the lookout for it.
GMAT assassins aren't born, they're made,
Rich
This question is a great example of a "Work Formula" question. Any time you have a question with two entities (people, machines, etc.) who can each do a particular job alone at a set rate, but work together - then you're dealing with the Work Formula.
The Work Formula: [AxB]/[A+B]
Just plug in the two times (in this case, 2 hours and 1/2 hour) in for A and B and you'll have the time it would take the two working together to finish the job.
Rahul's answer shows the math and the correct answer.
You'll likely see this concept once on Test Day (and it might be more complex than this question), so be on the lookout for it.
GMAT assassins aren't born, they're made,
Rich
- theCodeToGMAT
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Adding on Rich's comments, below are the steps to reach to that shortcut formula:
t = total time
A = Time of "A"
B = Time of "B"
1/t = 1/A + 1/B
1/t = (A+B)/(AB)
t = AB/(A+B)
t = total time
A = Time of "A"
B = Time of "B"
1/t = 1/A + 1/B
1/t = (A+B)/(AB)
t = AB/(A+B)
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- ganeshrkamath
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I suggest going for the general method that I follow for work-related problems:yumi2012 wrote:Got this problem wrong too. Thanks for your explanation in advance!
Small pump takes two hours to fill the tank.
So, in one hour it can fill half the tank.
Rate at which the small pump fills the tank = 1/2(V) per hour_________________(V is the volume of the tank)
Large pump can fill the tank in 1/2 hour
So, rate at which the large pump fills the tank = 1/(1/2) (V) per hour = 2V per hour
Their combined rate = (1/2)V + 2V per hour
= (5/2)V per hour
So, in one hour they can fill (5/2)V
To fill V, they would need 1/(5/2) = 2/5 hours
Choose C
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https://www.beatthegmat.com/first-attemp ... tml#688494
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Let the tank = 2 gallons.A small water pump would take 2 hours to fill an empty tank. A larger pump would take 1/2 hour to fill the same tank. How many hours would it take both pumps, working at their respective constant rate, to fill the empty tank if they began pumping at the same time?
1/4
1/3
2/5
5/4
3/2
Small pump's rate = w/t = 2/2 = 1 gallon per hour.
Large pump's rate = w/t = 2/(1/2) = 2*2 = 4 gallons per hour.
When elements work together, ADD THEIR RATES.
Combined rate for both pumps = 1+4 = 5 gallons per hour.
Thus:
Time for both pumps together = w/r = 2/5 hours.
The correct answer is C.
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I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
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