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

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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 ! 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!!

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.

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 \(t_2=21\)

I answered it incorrectly.
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!!

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.

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

ANSWER IS C

shouldn't be X=32500/16 ?
thanks,

Statement 1:
When X and Y together fill half the pool and Y alone fills the remaining half, the total time = 21 hours.
Implication:
If X and Y together fill the ENTIRE pool, the time will be LESS than 21 hours.
No way to determine the exact time.
INSUFFICIENT.

Statement 2:
When X and Y together fill half the pool and X alone fills the remaining half, the total time = 16 hours.
Implication:
If X and Y together fill the ENTIRE pool, the time will be LESS than 16 hours.
No way to determine the exact time.
INSUFFICIENT.

Statements combined:
Since half the pool = 37,500 liters, it is almost certain that the 21-hour time in Statement 1 is split between two times that divide evenly into 37,500.
Since 37,500 is divisible by 6 and 15, test a time of 6 hours for X and Y together to fill the first half of the pool and a time of 15 hours for Y alone to fill the remaining half, for a total time of 21 hours.
If X and Y together take 6 hours to pump in the first 37,500 liters, the rate for X and Y together = \(\frac{work}{time} = \frac{37,500}{6} = 6250\) liters per hour.
If Y takes 15 hours to pump in the remaining 37,500 liters, the rate for Y alone \(= \frac{work}{time} = \frac{37,500}{15} = 2500\) liters per hour.
Resulting rate for X alone = (rate for X and Y together) - (Y's rate alone) = 6250-2500 = 3750 liters per hour.

Do the values above satisfy Statement 2, which indicates a total time of 16 hours when X and Y fill half the pool and X alone fills the remaining half?
If X and Y together take 6 hours to fill the first half of the pool, the time for X alone -- working at a rate of 3750 liters per hour -- to fill the remaining half of the pool \(= \frac{work}{rate} = \frac{37,500}{3750} = 10\) hours, for a total time of 16 hours.
Statement 2 is satisfied.

Since the tested values satisfy both statements, we know that the time for X and Y together to fill half the pool = 6 hours, implying a total time of 12 hours for X and Y to fill the entire pool.
SUFFICIENT.

Question: R = R(x)+R(y) , T =? , W=75000, T = 75000/R , suff if we can find sum of Rate of x and y OR T = ?

Statement 1 :
Both fill half tank : R(x)+R(y) , t , 75000/2 = 37500 => At the rate of R(x) + R(y),it will take time "2t" to completely fill the tank i.e. 75000ltrs. => R(x) + R(y) = 37500/t

X stops Y fills the other half : R(y) , t(y) , 37500 => R(y) = 37500/t(y)

t + t(y) = 21 => t(y) = 21 - t

not suff, since R(x) = ? OR t(y)=?

Statement 2 :
Both fill half tank : R(x)+R(y) , t , 37500

Y stops X fills the other half : R(x) , t(x) , 37500 => R(x) = 37500/t(x)

t+t(x) = 16 => t(x) = 16 - t

not suff, since R(y) = ? OR t(x)=?

Both Statements :
We have R(y) = 37500/t(y), R(x) = 37500/t(x), t(y) = 21 - t , t(x) = 16 - t

R(x) + R(y) = 37500/t(x) + 37500/t(y)

37500/t = 37500/t(x) + 37500/t(y)

1/t = 1/t(x) + 1/t(y)

Since, we have t(x) and t(y) in terms of t, it is sufficient to find the value of t and thus T=2t , Thus ANSWER C


Verification :
1/t = 1/t(x) + 1/t(y) => t = t(x) t(y)/ t(x)+t(y)

t = (16 - t) (21 - t) / (37-2t)

37 - 2t = 336 - 37t - t^2

t^2 + 35t -299 = 0

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