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# An empty swimming pool with a capacity of 75,000 liters is

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An empty swimming pool with a capacity of 75,000 liters is [#permalink]

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01 Apr 2012, 16:06
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An empty swimming pool with a capacity of 75,000 liters is to be filled by hoses X and Y simultaneously. If the amount of water flowing from each hose is independent of the amount flowing from the other hose, how long, in hours, will it take to fill the pool?

(1) If hose X stopped filling the pool after hoses X and Y had filled half the pool, it would take 21 hours to fill the pool.
(2) If hose Y stopped filling the pool after hoses X and Y had filled half the pool, it would take 16 hours to fill the pool.
[Reveal] Spoiler: OA

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Re: Hoses X & Y [#permalink]

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01 Apr 2012, 16:30
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An empty swimming pool with a capacity of 75,000 liters is to be filled by hoses X and Y simultaneously. If the amount of water flowing from each hose is independent of the amount flowing from the other hose, how long, in hours, will it take to fill the pool?

(1) If hose X stopped filling the pool after hoses X and Y had filled half the pool, it would take 21 hours to fill the pool. After hose X stops, hose Y continues filling the remaining half of the pool alone, and we are told that it needs 21 hours for that, hence to fill the whole pool it needs 21*2=42 hours. We know the rate of Y, though know nothing about the rate of X. Not sufficient.

(2) If hose Y stopped filling the pool after hoses X and Y had filled half the pool, it would take 16 hours to fill the pool. Reverse case: after hose Y stops, hose X continues filling the remaining half of the pool alone, and we are told that it needs 16 hours for that, hence to fill the whole pool it needs 16*2=32 hours. We know the rate of X, though know nothing about the rate of Y. Not sufficient.

(1)+(2) We know the rates of both hose X and Y, hence we can calculate the time they'll need to fill the pool of 75,000 liters. Sufficient.

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Re: An empty swimming pool with a capacity of 75,000 liters is [#permalink]

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30 May 2013, 04:56
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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Re: An empty swimming pool with a capacity of 75,000 liters is [#permalink]

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31 May 2013, 08:55
I was a bit confused with this question. My interpretation of the time to fill to pool was that it was the total time. So the time would include the time taken for X and Y to fill the pool to half plus the time for Y (orX) to fill the other half.

Timica
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Re: An empty swimming pool with a capacity of 75,000 liters is [#permalink]

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02 Jun 2013, 05:47
timica wrote:
I was a bit confused with this question. My interpretation of the time to fill to pool was that it was the total time. So the time would include the time taken for X and Y to fill the pool to half plus the time for Y (orX) to fill the other half.

Timica

Consider this: the pool is to be filled by hoses X and Y simultaneously. The question is: how long, in hours, will it take to fill the pool?
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Re: An empty swimming pool with a capacity of 75,000 liters is [#permalink]

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09 Sep 2013, 13:16
Hi ! I know I am way past the time for this thread but I'll still give my thoughts for someone coming here in the future!

I find DS questions easier to comprehend once I write down the data in a form of equation (s). IN the given questions, lets take the respective rates of hoses X & Y to be r_x & r_y and the total time to be 't'. We need to find 't' , where t=75000/(r_x + r_y)

Once we write down the above equation, it becomes very clear that we need to find r_x & r_y together to be able to find 't'. Hence, we need both statements (1) & (2) together to solve the above. Hence, option C.

Thank you again for this awesome series brunel! I'll be looking forward to all the other juicy questions coming up!!
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Re: An empty swimming pool with a capacity of 75,000 liters is [#permalink]

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24 Sep 2013, 10:23
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Bunuel wrote:
timica wrote:
I was a bit confused with this question. My interpretation of the time to fill to pool was that it was the total time. So the time would include the time taken for X and Y to fill the pool to half plus the time for Y (orX) to fill the other half.

Timica

Consider this: the pool is to be filled by hoses X and Y simultaneously. The question is: how long, in hours, will it take to fill the pool?

Hi Bunuel! I too thought that 21 and 16 are total time and therefore wrote my equations as:-
1. 21 = [75k/2(x+y)] + [75k/2y]
2. 16 = [75k/2(x+y)] + [75k/2x]
k=1000, x = X's rate and y = Y's rate. This way too C will be the answer.
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Re: Hoses X & Y [#permalink]

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09 Nov 2013, 17:15
Bunuel wrote:
An empty swimming pool with a capacity of 75,000 liters is to be filled by hoses X and Y simultaneously. If the amount of water flowing from each hose is independent of the amount flowing from the other hose, how long, in hours, will it take to fill the pool?

(1) If hose X stopped filling the pool after hoses X and Y had filled half the pool, it would take 21 hours to fill the pool. After hose X stops, hose Y continues filling the remaining half of the pool alone, and we are told that it needs 21 hours for that, hence to fill the whole pool it needs 21*2=42 hours. We know the rate of Y, though know nothing about the rate of X. Not sufficient.

(2) If hose Y stopped filling the pool after hoses X and Y had filled half the pool, it would take 16 hours to fill the pool. Reverse case: after hose Y stops, hose X continues filling the remaining half of the pool alone, and we are told that it needs 16 hours for that, hence to fill the whole pool it needs 16*2=32 hours. We know the rate of X, though know nothing about the rate of Y. Not sufficient.

(1)+(2) We know the rates of both hose X and Y, hence we can calculate the time they'll need to fill the pool of 75,000 liters. Sufficient.

Bunuel, how is the question blindly giving us the rates of Y and X respectively in 1 and 2?

I interpreted (1) to say the following
t1/x + (1/y)*(t1+t2) = 1
t1 + t2 = 21
t1 = the time it takes both x and y to fill half of the pool
t1/x + 21/y = 1

Can you show me where I went wrong?
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Re: Hoses X & Y [#permalink]

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10 Nov 2013, 04:46
TooLong150 wrote:
Bunuel wrote:
An empty swimming pool with a capacity of 75,000 liters is to be filled by hoses X and Y simultaneously. If the amount of water flowing from each hose is independent of the amount flowing from the other hose, how long, in hours, will it take to fill the pool?

(1) If hose X stopped filling the pool after hoses X and Y had filled half the pool, it would take 21 hours to fill the pool. After hose X stops, hose Y continues filling the remaining half of the pool alone, and we are told that it needs 21 hours for that, hence to fill the whole pool it needs 21*2=42 hours. We know the rate of Y, though know nothing about the rate of X. Not sufficient.

(2) If hose Y stopped filling the pool after hoses X and Y had filled half the pool, it would take 16 hours to fill the pool. Reverse case: after hose Y stops, hose X continues filling the remaining half of the pool alone, and we are told that it needs 16 hours for that, hence to fill the whole pool it needs 16*2=32 hours. We know the rate of X, though know nothing about the rate of Y. Not sufficient.

(1)+(2) We know the rates of both hose X and Y, hence we can calculate the time they'll need to fill the pool of 75,000 liters. Sufficient.

Bunuel, how is the question blindly giving us the rates of Y and X respectively in 1 and 2?

I interpreted (1) to say the following
t1/x + (1/y)*(t1+t2) = 1
t1 + t2 = 21
t1 = the time it takes both x and y to fill half of the pool
t1/x + 21/y = 1

Can you show me where I went wrong?

It should be $$t_1(\frac{1}{x}+\frac{1}{y}) + t_2(\frac{1}{y}) = 1$$, where $$t_2=21$$. We know that $$t_2(\frac{1}{y}) = \frac{1}{2}$$, thus $$\frac{21}{y} = \frac{1}{2}$$ --> $$y = 42$$ hours.
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Re: An empty swimming pool with a capacity of 75,000 liters is [#permalink]

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03 Aug 2014, 12:39
Bunuel wrote:
TooLong150 wrote:
Bunuel wrote:
An empty swimming pool with a capacity of 75,000 liters is to be filled by hoses X and Y simultaneously. If the amount of water flowing from each hose is independent of the amount flowing from the other hose, how long, in hours, will it take to fill the pool?

(1) If hose X stopped filling the pool after hoses X and Y had filled half the pool, it would take 21 hours to fill the pool. After hose X stops, hose Y continues filling the remaining half of the pool alone, and we are told that it needs 21 hours for that, hence to fill the whole pool it needs 21*2=42 hours. We know the rate of Y, though know nothing about the rate of X. Not sufficient.

(2) If hose Y stopped filling the pool after hoses X and Y had filled half the pool, it would take 16 hours to fill the pool. Reverse case: after hose Y stops, hose X continues filling the remaining half of the pool alone, and we are told that it needs 16 hours for that, hence to fill the whole pool it needs 16*2=32 hours. We know the rate of X, though know nothing about the rate of Y. Not sufficient.

(1)+(2) We know the rates of both hose X and Y, hence we can calculate the time they'll need to fill the pool of 75,000 liters. Sufficient.

Bunuel, how is the question blindly giving us the rates of Y and X respectively in 1 and 2?

I interpreted (1) to say the following
t1/x + (1/y)*(t1+t2) = 1
t1 + t2 = 21
t1 = the time it takes both x and y to fill half of the pool
t1/x + 21/y = 1

Can you show me where I went wrong?

It should be $$t_1(\frac{1}{x}+\frac{1}{y}) + t_2(\frac{1}{y}) = 1$$, where $$t_2=21$$. We know that $$t_2(\frac{1}{y}) = \frac{1}{2}$$, thus $$\frac{21}{y} = \frac{1}{2}$$ --> $$y = 42$$ hours.

I think that they mean that $$t_1 + t_2 = 21$$ and not $$t_2=21$$
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Re: An empty swimming pool with a capacity of 75,000 liters is [#permalink]

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14 Aug 2014, 03:56
Bunuel wrote:
An empty swimming pool with a capacity of 75,000 liters is to be filled by hoses X and Y simultaneously. If the amount of water flowing from each hose is independent of the amount flowing from the other hose, how long, in hours, will it take to fill the pool?

(1) If hose X stopped filling the pool after hoses X and Y had filled half the pool, it would take 21 hours to fill the pool. After hose X stops, hose Y continues filling the remaining half of the pool alone, and we are told that it needs 21 hours for that, hence to fill the whole pool it needs 21*2=42 hours. We know the rate of Y, though know nothing about the rate of X. Not sufficient.

(2) If hose Y stopped filling the pool after hoses X and Y had filled half the pool, it would take 16 hours to fill the pool. Reverse case: after hose Y stops, hose X continues filling the remaining half of the pool alone, and we are told that it needs 16 hours for that, hence to fill the whole pool it needs 16*2=32 hours. We know the rate of X, though know nothing about the rate of Y. Not sufficient.

(1)+(2) We know the rates of both hose X and Y, hence we can calculate the time they'll need to fill the pool of 75,000 liters. Sufficient.

My thought was:
We know that first half was filled by both X and Y. and Y filled for 21 hrs. So, 75000/2 ltr was filled by both in first half and Y filled for 21 hrs. (total 42 hrs) we can check that how much liters can X fill in the first half of the tank!!
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An empty swimming pool with a capacity of 75,000 liters is [#permalink]

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29 Feb 2016, 22:01
Hi Bunuel

My understanding of the question is similar to others who have posted.

Statement 1 states:
(1) If hose X stopped filling the pool after hoses X and Y had filled half the pool, it would take 21 hours to fill the pool.
Therefore:
t1+t2 = 21 hours, t1= 32,500*[Rate(x) + Rate (y)], and t2 = 32,500 * [Rate(y)]

Same logic would apply for statement 2.
Statement 2 states:
(2) If hose Y stopped filling the pool after hoses X and Y had filled half the pool, it would take 16 hours to fill the pool.

Therefore:
t1+t2 = 16 hours, t1= 32,500*[Rate(x) + Rate (y)], and t2 = 32,500 * [Rate(x)]

Both statements clearly state that it would take their respective amount of times (21hrs and 16 hrs), if both hoses filled half the pool together, and then one hose continued the job alone to fill the other half of the pool.

Thanks.
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Re: An empty swimming pool with a capacity of 75,000 liters is [#permalink]

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01 Mar 2016, 05:19
ashakil3 wrote:
Hi Bunuel

My understanding of the question is similar to others who have posted.

Statement 1 states:
(1) If hose X stopped filling the pool after hoses X and Y had filled half the pool, it would take 21 hours to fill the pool.
Therefore:
t1+t2 = 21 hours, t1= 32,500*[Rate(x) + Rate (y)], and t2 = 32,500 * [Rate(y)]

Same logic would apply for statement 2.
Statement 2 states:
(2) If hose Y stopped filling the pool after hoses X and Y had filled half the pool, it would take 16 hours to fill the pool.

Therefore:
t1+t2 = 16 hours, t1= 32,500*[Rate(x) + Rate (y)], and t2 = 32,500 * [Rate(x)]

Both statements clearly state that it would take their respective amount of times (21hrs and 16 hrs), if both hoses filled half the pool together, and then one hose continued the job alone to fill the other half of the pool.

Thanks.

Sorry, but I do not understand what you've written there. Generally time*rate = job done, not time = job*rate.

Notice also that we don't know how much time is needed for hoses X and Y to fill half the pool.
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Re: An empty swimming pool with a capacity of 75,000 liters is [#permalink]

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05 Mar 2016, 13:32
Bunuel wrote:
ashakil3 wrote:
Hi Bunuel

My understanding of the question is similar to others who have posted.

Statement 1 states:
(1) If hose X stopped filling the pool after hoses X and Y had filled half the pool, it would take 21 hours to fill the pool.
Therefore:
t1+t2 = 21 hours, t1= 32,500*[Rate(x) + Rate (y)], and t2 = 32,500 * [Rate(y)]

Same logic would apply for statement 2.
Statement 2 states:
(2) If hose Y stopped filling the pool after hoses X and Y had filled half the pool, it would take 16 hours to fill the pool.

Therefore:
t1+t2 = 16 hours, t1= 32,500*[Rate(x) + Rate (y)], and t2 = 32,500 * [Rate(x)]

Both statements clearly state that it would take their respective amount of times (21hrs and 16 hrs), if both hoses filled half the pool together, and then one hose continued the job alone to fill the other half of the pool.

Thanks.

Sorry, but I do not understand what you've written there. Generally time*rate = job done, not time = job*rate.

Notice also that we don't know how much time is needed for hoses X and Y to fill half the pool.

Bunuel

Sorry, my "*" sign should be a "/" sign.

So for statement (1): t1+t2 = 21 hours, t1= 32,500 / [Rate(x) + Rate (y)], and t2 = 32,500 / [Rate(Y)]
And for statement (2): t1+t2 = 16 hours, t1= 32,500 / [Rate(x) + Rate (y)], and t2 = 32,500 / [Rate(X)]

Therefore, "21 hours" is the total time it takes to fill the pool if X&Y hoses work together for half the pool, and Y fills the remaining half of the pool. While in statement 2 it states "16 hours" is the total time it takes to fill the pool, if X&Y hoses work together to fill half the pool, and X fills the remaining half of the pool.
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An empty swimming pool with a capacity of 75,000 liters is [#permalink]

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01 Aug 2016, 05:52
enigma123 wrote:
An empty swimming pool with a capacity of 75,000 liters is to be filled by hoses X and Y simultaneously. If the amount of water flowing from each hose is independent of the amount flowing from the other hose, how long, in hours, will it take to fill the pool?

(1) If hose X stopped filling the pool after hoses X and Y had filled half the pool, it would take 21 hours to fill the pool.
(2) If hose Y stopped filling the pool after hoses X and Y had filled half the pool, it would take 16 hours to fill the pool.

Let rate of X hose be x and Y hose be y
(1) If hose X stopped filling the pool after hoses X and Y had filled half the pool, it would take 21 hours to fill the pool.
SO this tells us that Half pool is filled ; therefore we can assume that Y is only effectively doing only half work and taking 21 hours to do that half work
y* 21= half of 75000 = 32500
y=32500/21
Now we know the rate of hose Y ; rate of hose X is missing
INSUFFICIENT

(2) If hose Y stopped filling the pool after hoses X and Y had filled half the pool, it would take 16 hours to fill the pool.
SO this tells us that Half pool is filled ; therefore we can assume that X is only effectively doing only half work and taking 16 hours to do that half work.
x* 16= half of 75000=32500
y=32500/16
Now we know the rate of hose Y ; rate of hose X is missing
INSUFFICIENT

Merge both now we know the combined rate of x and y
( x + y) * time = total work = 75000

Time = 75000/x+y
Although x+y looks like a weird number but we know it is "32500/21 + 32500/16"

SUFFICIENT

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