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A small water pump would take 2 hours to fill an empty tank

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A small water pump would take 2 hours to fill an empty tank  [#permalink]

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07 Feb 2012, 06:00
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Can someone assist me with solving this question?

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 rates, to fill the empty tank if they began pumping at the same time?

A) 1/4
B) 1/3
C) 2/5
D) 5/4
E) 3/2
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Posts: 52902

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07 Feb 2012, 06:09
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domu904 wrote:
Can someone assist me with solving this question?

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 rates, to fill the empty tank if they began pumping at the same time?

A) 1/4
B) 1/3
C) 2/5
D) 5/4
E) 3/2

Rate of the small pump is 1/2 tank/hour (rate is reciprocal of time);
Rate of the larger pump is 2 tank/hour;

Combined rate of the two pumps is 1/2+2=5/2 tank/hour, hence together they will fill the empty tank in 1/(5/2)=2/5 hours (time=job/rate).

Theory on work/rate problems:
two-consultants-can-type-up-a-report-126155.html?hilit=know%20rate%20work%20reciprocal#p1030079

Hope it helps.

P.S. Please post PS questions in the PS subforum: gmat-problem-solving-ps-140/ and DS questions in the DS subforum: gmat-data-sufficiency-ds-141/

No posting of PS/DS questions is allowed in the main Math forum.
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Re: A small water pump would take 2 hours to fill an empty tank  [#permalink]

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10 Jan 2015, 12:31
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Hi All,

We're given the rates of two entities that will share a job together - this is the standard "set-up" for a Work Formula question.

Work Formula = (A)(B)/(A+B) where A and B are the respective amounts of time needed to individually complete a job.

Pump A = 2 hours to fill a tank
Pump B = 1/2 hour to fill a tank

Working together, it takes....

(2)(1/2)/(2 + 1/2) = 1/2.5 hours to fill the tank together...

1/2.5 = 2/5 hours

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Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ *****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***** Intern Joined: 29 Nov 2015 Posts: 13 Re: A small water pump would take 2 hours to fill an empty tank [#permalink] Show Tags 29 Dec 2015, 10:08 Bunuel wrote: domu904 wrote: Can someone assist me with solving this question? 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 rates, to fill the empty tank if they began pumping at the same time? A) 1/4 B) 1/3 C) 2/5 D) 5/4 E) 3/2 Rate of the small pump is 1/2 tank/hour (rate is reciprocal of time); Rate of the larger pump is 2 tank/hour; Combined rate of the two pumps is 1/2+2=5/2 tank/hour, hence together they will fill the empty tank in 1/(5/2)=2/5 hours (time=job/rate). Answer: C. Hi, the logic I used was pretty much the same as yours, still Idk where I went wrong... small pump fills 1 tank in 2 hours -> 1/2 tank in 1 hour -> 1/4 tank in 1/2 hour big pump fills 1 tank in 1/2 hour 1/4 + 1 = 5/4 work which will take 4/5 hours EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 13540 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: A small water pump would take 2 hours to fill an empty tank [#permalink] Show Tags 29 Dec 2015, 22:46 1 Hi sarathvr, With the work that you've done, you have calculated how much of the tank would be filled in 1/2 an hour by the two pumps (working together). In 1/2 hour: The small pump would fill 1/4 of the tank The large pump would fill 1/1 of the tank Combined, that is 1/4 + 4/4 = 5/4 of the tank in 1/2 an hour. This means that the two pumps would OVER-FILL the tank in 1/2 an hour. By extension, it would take LESS than 1/2 an hour to fill the tank, so the answer CAN'T be 4/5 of an hour. If you're going to use this approach, then you would have to MULTIPLY both sides by 4/5.... (5/4 of a tank)(4/5) = (1/2 hour)(4/5) 20/20 of a tank = 4/10 of an hour 1 tank = 2/5 of an hour GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Re: A small water pump would take 2 hours to fill an empty tank  [#permalink]

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30 Dec 2015, 06:33
EMPOWERgmatRichC wrote:
Hi sarathvr,

With the work that you've done, you have calculated how much of the tank would be filled in 1/2 an hour by the two pumps (working together).

In 1/2 hour:
The small pump would fill 1/4 of the tank
The large pump would fill 1/1 of the tank

Combined, that is 1/4 + 4/4 = 5/4 of the tank in 1/2 an hour. This means that the two pumps would OVER-FILL the tank in 1/2 an hour. By extension, it would take LESS than 1/2 an hour to fill the tank, so the answer CAN'T be 4/5 of an hour.

If you're going to use this approach, then you would have to MULTIPLY both sides by 4/5....

(5/4 of a tank)(4/5) = (1/2 hour)(4/5)
20/20 of a tank = 4/10 of an hour
1 tank = 2/5 of an hour

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

OK yes! I didn't realise the over-full thing, so yeah that made sense.

But I still didn't understand the logic behind multiplying by 4/5 :/
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Re: A small water pump would take 2 hours to fill an empty tank  [#permalink]

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30 Dec 2015, 10:16
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Hi sarathvr,

The math that you did calculated the time it takes to fill 5/4 of a tank, but the question asks you to fill 4/4 of a tank. Mathematically, since we're dealing with rates, to decrease 5/4 to 4/4 we have to multiply by 4/5. Since we're multiplying one side of the 'equation' by 4/5, we have to multiply the other side by 4/5 also...

(5/4 of a tank)(4/5) = (1/2 hour)(4/5)
20/20 of a tank = 4/10 of an hour
1 tank = 2/5 of an hour

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Re: A small water pump would take 2 hours to fill an empty tank  [#permalink]

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21 Jun 2017, 22:35
Efficiency of small water pump $$= 50$$%, i.e., it can fill $$50$$% of the tank in an hour.

Similarly, efficiency of the larger water pump $$= 200$$%, i.e, it can fill the tank twice in an hour.

So, the time taken to fill the tank, which is the inverse of efficiency, when both work simultaneously $$= \frac{100}{250} = \frac{20}{50} = \frac{2}{5}$$.
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A small water pump would take 2 hours to fill an empty tank  [#permalink]

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16 Jul 2017, 07:17
1
domu904 wrote:
Can someone assist me with solving this question?

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 rates, to fill the empty tank if they began pumping at the same time?

A) 1/4
B) 1/3
C) 2/5
D) 5/4
E) 3/2

Time taken per hour by small pump $$= \frac{1}{2}$$

Time taken per hour by large pump $$= 2$$

Total time taken $$= \frac{1}{2} + 2 = \frac{4+1}{2} = \frac{5}{2}$$

Total work done $$= \frac{2}{5}$$

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Re: A small water pump would take 2 hours to fill an empty tank  [#permalink]

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05 Sep 2018, 09:49
Before you launch into the math, take a look at the answer choices. Only two answer choices are possible - B and C. Depending on time, you might want to guess quickly and move on. Here is how you know.

If the two pumps are working together, they will complete the job faster than either pump working alone. So, the two pumps will fill the tank faster than 0.5 hours. Eliminate D and E

Consider this - two big pumps fill the tank in half of the time that one big pump takes to fill the tank. So, two big pumps fill the tank in 0.25 hours. The small pump is slower, so a small pump plus a big pump must take longer than 0.25 hours. Eliminate A.

Depending one time, guess or do enough math to eliminate B or C.

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Re: A small water pump would take 2 hours to fill an empty tank   [#permalink] 05 Sep 2018, 09:49
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