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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, 07:00

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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 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).

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

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07 Jan 2014, 04:59

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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, 07:21

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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

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29 Dec 2015, 11:08

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

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

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29 Dec 2015, 23:46

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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

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

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30 Dec 2015, 07:33

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 :/

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

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30 Dec 2015, 11:16

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Expert's post

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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