Two water pumps, working simultaneously at their respective constant

jasminelin this is where you went astray:


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.

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

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