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Two water pumps, working simultaneously at their respective

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Two water pumps, working simultaneously at their respective constant rates, took exactly four hours to fill a certain swimming pool. If the constant rate of one pump was 1.5 times the constant rate of the other, how many hours would it have taken the faster pump to fill the pool if it had worked alone at it's constant rate?

A. 5
B. 16/3
C. 11/2
D. 6
E. 20/3

Work rate problems are my weakest area. For whatever reason I get mixed up on these problem. Even knowing the answer to this question I can't figure out how it comes out to that answer. Any help would be great, thanks!
[Reveal] Spoiler: OA

Last edited by Bunuel on 12 Jul 2013, 07:02, edited 1 time in total.
Renamed the topic and edited the question.
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kmasonbx wrote:
Two water pumps, working simultaneously at their respective constant rates, took exactly four hours to fill a certain swimming pool. If the constant rate of one pump was 1.5 times the constant rate of the other, how many hours would it have taken the faster pump to fill the pool if it had worked alone at it's constant rate?

A. 5
B. 16/3
C. 11/2
D. 6
E. 20/3

Work rate problems are my weakest area. For whatever reason I get mixed up on these problem. Even knowing the answer to this question I can't figure out how it comes out to that answer. Any help would be great, thanks!


Say the rate of the faster pump is x pool/hour, then the rate of the slower pump would be x/1.5=2x/3 pool/hour.

Since, the combined rate is 1/4 pool/hour, then we have that x+2x/3=1/4 --> x=3/20 pool hour.

The time is reciprocal of the rate, therefore it would take 20/3 hours the faster pump to fill the pool working alone.

Answer: E.

Theory on work/rate problems: work-word-problems-made-easy-87357.html

All DS work/rate problems to practice: search.php?search_id=tag&tag_id=46
All PS work/rate problems to practice: search.php?search_id=tag&tag_id=66

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Re: Two water pumps, working simultaneously at their respective [#permalink]

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New post 12 Jul 2013, 09:01
i am little confused. If i take slower pump as X then 1/X + 1/1.5X = 1/4 which would result X = 20/3 and so faster pump as 10..... where i am going wrong...
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New post 12 Jul 2013, 09:07
AMITAGARWAL2 wrote:
i am little confused. If i take slower pump as X then 1/X + 1/1.5X = 1/4 which would result X = 20/3 and so faster pump as 10..... where i am going wrong...


In my solution x is the rate in your solution x is the time.

In your solution x is the time of the faster pump and 1.5x is the time of the slower pump (faster pump needs less time).

Hope it's clear.
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New post 12 Jul 2013, 10:34
yes it does. Thanks...
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kmasonbx wrote:
Two water pumps, working simultaneously at their respective constant rates, took exactly four hours to fill a certain swimming pool. If the constant rate of one pump was 1.5 times the constant rate of the other, how many hours would it have taken the faster pump to fill the pool if it had worked alone at it's constant rate?

A. 5
B. 16/3
C. 11/2
D. 6
E. 20/3

Work rate problems are my weakest area. For whatever reason I get mixed up on these problem. Even knowing the answer to this question I can't figure out how it comes out to that answer. Any help would be great, thanks!


sol:

Rates be A and B

(A+B) * Time = Work
(A+B) * 4 = 1 ---->eq 1

A= 3B/2 ----->eq 2

substituting eq 2 in eq 1

B = 1/10 --->eq 3

substituting eq 3 in eq 2

A= 3/20

Time= work/rate
= 1/(3/20) =>20/3
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New post 25 Sep 2013, 04:13
I did,
A+B = 4
A = 1.5B

4-B = 1.5B => B = 8/5

Why is this wrong?
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Skag55 wrote:
I did,
A+B = 4
A = 1.5B

4-B = 1.5B => B = 8/5

Why is this wrong?


We are told that "two water pumps, working simultaneously at their respective constant rates, took exactly four hours to fill a certain swimming pool".

If one pump needs A hours to fill the pool (rate=1/A) and another need B hours to fill the same pool (rate=1/B), then 1/A + 1/B = 1/4.

Solving 1/A + 1/B = 1/4 and A = 1.5B gives A=10 and B=20/3.

Check the links provided here: two-water-pumps-working-simultaneously-at-their-respective-155865.html#p1245761 for more.
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New post 01 Sep 2014, 19:06
Quote:
I did,
A+B = 4
A = 1.5B

4-B = 1.5B => B = 8/5

Why is this wrong?


A+B=(1/T)
NOT
A+B=T

Per formula,
(A+B)T = 1 where A is rate of pump A, B is rate of pump B, T time to complete, and 1 marking completion.
[(A+B)T]/T = 1/T
(A+B) = (1/T)

With B being the rate of the faster pump, B = (3/2)A

A + (3/2)A = (1/4)
(5/2)A = 1/4
A = 1/10
B = 3/20

B = 1/T
(3/20) = 1/T
T = (20/3)
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AMITAGARWAL2 wrote:
yes it does. Thanks...


Let me elaborate the math so that it's absolutely clear:

Let's calculate the combined rate first:

Rate x Time = Work
Rate x 4 = 1 [It takes 4 hours for both the pumps to fill up the pool]
Rate = 1/4 [So, 1/4 is the rate for the pumps working together]

Now, the let's assume the rate for the slower pump is x ; so the rate for the faster pump will be 1.5x

According to our previous calculations,
Slower pump + faster pump = 1/4
x + 1.5x = 1/4
2.5x = 1/4
x = 1/10 [slower pump's rate]

so, the faster pump's rate is 1/10 x 1.5 = 3/20

Now let's calculate the time it will take for the faster pump

Rate x Time = Work
3/20 x Time = 1
Time = 1 x 20/3 = 20/3 the answer :)
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New post 14 Feb 2015, 13:38
kmasonbx wrote:
Two water pumps, working simultaneously at their respective constant rates, took exactly four hours to fill a certain swimming pool. If the constant rate of one pump was 1.5 times the constant rate of the other, how many hours would it have taken the faster pump to fill the pool if it had worked alone at it's constant rate?

A. 5
B. 16/3
C. 11/2
D. 6
E. 20/3

Work rate problems are my weakest area. For whatever reason I get mixed up on these problem. Even knowing the answer to this question I can't figure out how it comes out to that answer. Any help would be great, thanks!



fast pump takes x hour
Slow pump takes 1.5x hour

so

1/x+1/1.5x = 1/4

> (1.5+1)/1.5x = 1/4
> 2.5/1.5x = 1/4
> 1.5 x = 10
>x = 10/1.5
>x = 20/3


Somebody confirm whether this is a right approach to do this type of problem or not. Thanks
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New post 14 Feb 2015, 20:23
Hi Salvetor,

Yes, your approach is correct. In 'Work' questions, there are usually several different ways to organize the given information, but they all end up involving a ratio at some point.

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New post 05 Feb 2016, 18:29
Salvetor wrote:
kmasonbx wrote:
Two water pumps, working simultaneously at their respective constant rates, took exactly four hours to fill a certain swimming pool. If the constant rate of one pump was 1.5 times the constant rate of the other, how many hours would it have taken the faster pump to fill the pool if it had worked alone at it's constant rate?

A. 5
B. 16/3
C. 11/2
D. 6
E. 20/3

Work rate problems are my weakest area. For whatever reason I get mixed up on these problem. Even knowing the answer to this question I can't figure out how it comes out to that answer. Any help would be great, thanks!



fast pump takes x hour
Slow pump takes 1.5x hour

so

1/x+1/1.5x = 1/4

> (1.5+1)/1.5x = 1/4
> 2.5/1.5x = 1/4
> 1.5 x = 10
>x = 10/1.5
>x = 20/3


Somebody confirm whether this is a right approach to do this type of problem or not. Thanks

I got all of this, and I get the whole logic, even why you have to flip etc. The only part I didn't get is why 1/x + 1/1.5x gives you a numerator (1.5+1)/1.5x rather than (1.5x+x)/1.5x.......I get the denominator, it's just the numerator part which confuses me, seems like I missed a fundamental concept in fractions.
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Re: Two water pumps, working simultaneously at their respective [#permalink]

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New post 06 Feb 2016, 09:15
How would you solve this problem by saying the faster pump 1.5x and slower x. I cant seem to figure that out.
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Re: Two water pumps, working simultaneously at their respective [#permalink]

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New post 06 Feb 2016, 09:48
xLUCAJx wrote:
How would you solve this problem by saying the faster pump 1.5x and slower x. I cant seem to figure that out.


Plug in some values-
Attachment:
Plug in.PNG
Plug in.PNG [ 2 KiB | Viewed 3119 times ]


Quote:
Two water pumps, working simultaneously at their respective constant rates, took exactly four hours to fill a certain swimming pool.


Capacity of the swimming pool is -

5*4 = 20

Quote:
how many hours would it have taken the faster pump to fill the pool if it had worked alone at it's constant rate?


The faster pump is pump B, so time required by fill the swimming pool alone will be = Total Capacity of the pool/Efficiency of Pipe B

20/3

Hence answer is (E)
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Re: Two water pumps, working simultaneously at their respective   [#permalink] 06 Feb 2016, 09:48
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