How many hours to fill this water tank?

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yumi2012: Senior | Next Rank: 100 Posts; Posts: 64; Joined: Mon Jul 23, 2012 1:59 pm; Thanked: 1 times

by yumi2012 » Sun Nov 17, 2013 11:26 pm

Got this problem wrong too. Thanks for your explanation in advance!

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Source: Beat The GMAT — Problem Solving | Sun Nov 17, 2013 11:26 pm

theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

by theCodeToGMAT » Sun Nov 17, 2013 11:32 pm

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]

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by [email protected] » Mon Nov 18, 2013 12:01 am

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.

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Rich

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theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

by theCodeToGMAT » Mon Nov 18, 2013 12:11 am

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)

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ganeshrkamath: Master | Next Rank: 500 Posts; Posts: 283; Joined: Sun Jun 23, 2013 11:56 pmFollowed by: 26 members; Location: Bangalore, India; Thanked: 97 times; GMAT Score:750

by ganeshrkamath » Mon Nov 18, 2013 12:36 am

yumi2012 wrote:Got this problem wrong too. Thanks for your explanation in advance!

I suggest going for the general method that I follow for work-related problems:

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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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Nov 18, 2013 3:21 am

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

Let the tank = 2 gallons.
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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