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Irising
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Two water pumps, working simultaneously at their respective constant   12 Nov 2020, 09:14
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Irising
I read quite a few solutions and they all have the following equation set up: 1/x+1/1.5x=1/4. But I have 1/x+1/1.5x=4. I don't understand why "x" is time. "x" to me is rate because the question states "constant rate of one pump was 1.5 times the constant rate of the other".

Can Bunuel or someone else please help? Thanks!

x is an unknown and you can denote by x either time or rate, it's your choice. Doesn't really matter.

If you say x is the rate, then you get: x + 2x/3 = 1/4. My solution here uses x as the rate: https://gmatclub.com/forum/two-water-pu ... l#p1245761

If you say x is the time, then you get: 1/x + 2/(3x) = 1/4.

In any case notice that we sum the rates.

Thank you for your reply! Please bare with me as I am still trying to understand the problem. When you say "we sum rates", do you also imply that we cannot sum time? In my equation, I set x as rate. Then I thought 1/x must be time (work/rate=time). And based on that, I sum time to solve for x: 1/x+1/(1.5x)=4, time of the slow pump+time of the fast pump=total time. There must be something wrong with my logic here but I can't seem to figure it out.
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Two water pumps, working simultaneously at their respective constant   12 Nov 2020, 10:08
Wow, thank you very much for your help Bunuel
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Two water pumps, working simultaneously at their respective constant   10 Feb 2022, 18:41
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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!

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.

[/textarea]

slow pump works at a rate of 1x, fast pump works at a rate of 1.5x
slow pump does 1/3 of the job in 4 hours, fast pump does 2/3 of the job in 4 hours
Thus, for fast pump to accomplish the remaining 1/3 of the job, it would take 6 hours.
Where does this go wrong?
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Two water pumps, working simultaneously at their respective constant   11 Feb 2022, 17:31
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jasminelin this is where you went astray:
jasminelin
slow pump does 1/3 of the job in 4 hours, fast pump does 2/3 of the job in 4 hours

Based on your inference, the fast pump is twice as fast as the slow pump (2/3 is twice as much as 1/3).
But, we were told that the fast pump is only 1.5 times as fast as the slow pump. So, in any given amount of time, the fast pump should do three-halves (3/2) as much work as the slow pump does. Not twice as much.
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Two water pumps, working simultaneously at their respective constant   01 Jul 2023, 03:11
Hi experts, could anyone help to clarify why is faster pump's rate is x and not 1.5x here?
Also not sure why answer is the same regardless of faster pump rate is x or 1.5x? Thanks for your time in advanced.
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Two water pumps, working simultaneously at their respective constant   01 Jul 2023, 04:04
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Kimberly77
Hi experts, could anyone help to clarify why is faster pump's rate is x and not 1.5x here?
Also not sure why answer is the same regardless of faster pump rate is x or 1.5x? Thanks for your time in advanced.

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

APPROACH 1:

If you assume that 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 the reciprocal of the rate, therefore it would take 20/3 hours for the faster pump to fill the pool working alone.

Answer: E.

APPROACH 2:

If you assume that the RATE of the slower pump is x pool/hour, then the RATE of the faster pump would be 1.5x = 3x/2 pool/hour.

Since the combined rate is 1/4 pool/hour, then we have that x + 3x/2 = 1/4 --> x = 1/10 pool/hour. The RATE of the faster pump would be 3x/2 = 3/20 pool/hour.

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

Answer: E.

APPROACH 3:

If you assume that the TIME it takes for the slower pump to fill the pool is x hours, then the TIME it takes for the faster pump to fill the pool would be x/1.5 = 2x/3 hours. Consequently, the rates of the slower and faster pumps would be 1/x and 3/(2x) pool/hour respectively.

Since the combined rate is 1/4 pool/hour, then we have that 1/x + 3/(2x) = 1/4 --> x = 10 hours. The TIME it takes for the faster pump to fill the pool would be x/1.5 = 2x/3 = 20/3 hours.

Answer: E.

APPROACH 4:

If you assume that the TIME it takes for the faster pump to fill the pool is x hours, then the TIME it takes for the slower pump to fill the pool would be 1.5x = 3x/2 hours. Consequently, the rates of the faster and slower pumps would be 1/x and 2/(3x) pool/hour respectively.

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

Answer: E.

As you can see, you can denote x as either the rate or the time of the slower or faster pump. It will still yield the same answer.

Hope it helps.
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Two water pumps, working simultaneously at their respective constant   05 Jul 2023, 13:46
Bunuel
Kimberly77
Hi experts, could anyone help to clarify why is faster pump's rate is x and not 1.5x here?
Also not sure why answer is the same regardless of faster pump rate is x or 1.5x? Thanks for your time in advanced.

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

APPROACH 1:

If you assume that 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 the reciprocal of the rate, therefore it would take 20/3 hours for the faster pump to fill the pool working alone.

Answer: E.

APPROACH 2:

If you assume that the RATE of the slower pump is x pool/hour, then the RATE of the faster pump would be 1.5x = 3x/2 pool/hour.

Since the combined rate is 1/4 pool/hour, then we have that x + 3x/2 = 1/4 --> x = 1/10 pool/hour. The RATE of the faster pump would be 3x/2 = 3/20 pool/hour.

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

Answer: E.

APPROACH 3:

If you assume that the TIME it takes for the slower pump to fill the pool is x hours, then the TIME it takes for the faster pump to fill the pool would be x/1.5 = 2x/3 hours. Consequently, the rates of the slower and faster pumps would be 1/x and 3/(2x) pool/hour respectively.

Since the combined rate is 1/4 pool/hour, then we have that 1/x + 3/(2x) = 1/4 --> x = 10 hours. The TIME it takes for the faster pump to fill the pool would be x/1.5 = 2x/3 = 20/3 hours.

Answer: E.

APPROACH 4:

If you assume that the TIME it takes for the faster pump to fill the pool is x hours, then the TIME it takes for the slower pump to fill the pool would be 1.5x = 3x/2 hours. Consequently, the rates of the faster and slower pumps would be 1/x and 2/(3x) pool/hour respectively.

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

Answer: E.

As you can see, you can denote x as either the rate or the time of the slower or faster pump. It will still yield the same answer.

Hope it helps.

Thank you so much Bunuel and it make sense now. You are a STAR :please: :thumbsup:
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Two water pumps, working simultaneously at their respective constant   19 Sep 2023, 15:09
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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

[spoiler=]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
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