An empty swimming pool with a capacity of 100,000 liters is to be fill

Question

An empty swimming pool with a capacity of 100,000 liters is to be filled by hoses A and B simultaneously, with both hoses starting at the same time and flowing constantly until the pool is full. If the amount of water flowing from each hose is independent from the amount flowing from the other hose, how long will it take to fill the pool?

(1) If hose A stopped filling the pool after hoses A and B had filled 1/3 of the pool, it would take 22 hours for hose B to finish filling the pool. 
(2) If hose B stopped filling the pool after hoses A and B had filled 1/2 of the pool, it would take 17 hours for hose A to finish filling the pool.

walker · Answer

C

We need to know rate for each hoses. First statement gives us rate for B, second statement gives us rate for A. So, C.

If you want to know how to calculate:

1) 22 hours * 3/2 = 33 hours (it would take for hose B to fill the empty pool)
2) 17 hours * 2/1 = 34 hours (it would take for hose A to fill the empty pool)

if both hoses work together:
t*1/33 + t*1/34 = 1 ---> t = 33*34/(33+34) ~ 33.5 hours

Economist · Answer

Initially was thinking about D. Because if we know the rate of one hose then we can set up an equation for the other hose as the amount of work done by both hoses is given ( eg. 1/3 in case of stmt 1 )
However, we can only set such equation IF we know for how much time were the two hoses operating to fill 1/3 of the pool.

So it should be C

pleonasm · Answer

Yep absolutely. It's a great trap though and I fell into it.

GMAT TIGER · Answer

Since the capacity of the pool, 100,000 liters, is given, we can get the rate of A and B from each of the statement.

Should be D.

PTK · Answer

Tiger, please advise what is wrong in my calculations:

Total work is 100,000 litres:
a-rate of A hose 
b-rate of B hose 
100,000/a- time for A hose alone to fill the pool 
100,000/b- time for B hose alone to fill the pool

We are asked to find 100,000/(a+b),  which reduces to the question what is a+b.

in 1) we are given that after filling a part (1/3 of pool) B worked alone and for a given period of time filled the pool in 22 hours. , so we can calculate b.
we are not provided how much time did it take A and B hose to fill 1/3 of pool, or 33,333 litres., so the 33,333/(a+b)=x hours. hence not sufficeint.

in 2) we are told that it will take hose A 17 hours to fill 50,000 litres of pool, we can calculate a. 
50,000/(a+b)=y hours, not sufficient. not suff.

1)& 2) both rates are provided, thus sufficeint to calculate total amount of time. (a+b) , hence C.

jko · Answer

Pkit, you're correct. Each answer choice only gives you enough information to solve for the rate of one hose.

In order to solve the problem we need to be able to calculate the total rate either directly or indirectly (by finding the rate of both hoses and adding the rates).

longhaul123 · Answer

what is the OA to this question. IMO the answer is D because in each of this statement you can find the individual rates.So answer is D

Bunuel · Answer

The OA is C. Check Walker's solution above. Also, check very similar question here: https://gmatclub.com/forum/an-empty-swi ... 30024.html Hope it helps.

hicely51 · Answer

Thanks for the above posts,

The quantity of your pool is a calculation of your swimming pool's dimensions extended by your pool's average intensity.

CEdward · Answer

VeritasKarishma

Can you explain the specific formula here for calculating this?

KarishmaB · Answer

CEdward

There is only one basic formula of work-rate:

Work = Rate * Time
Also, remember rate is additive. So combined rate = rate1 + rate2

(1) If hose A stopped filling the pool after hoses A and B had filled 1/3 of the pool, it would take 22 hours for hose B to finish filling the pool.

If 1/3rd pool is full, 2/3rd is remaining. So work to be done is 2/3rd pool.
Time taken by B alone for this work = 22 hrs
Rate of B = Work/time = (2/3)/22 = 1/33rd pool/hr

(2) If hose B stopped filling the pool after hoses A and B had filled 1/2 of the pool, it would take 17 hours for hose A to finish filling the pool.
If 1/2 the pool is full, 1/2 is remaining. Work to be done = 1/2 pool
Time taken by A alone for this work = 17 hrs
Rate of A = Work/Time = (1/2)/17 = 1/34th pool/hr

Combined rate of A and B = 1/33 + 1/34 = 67/33*34

Time taken = Work/Rate = 1/(67/33*34) = 33*34/67 = 16.7 hrs

Obviously, you don't need to calculate all this if you understand that each statement gives you rate of one hose and both together will give you combined rate and hence time taken when working together.

zjhon · Answer

We are given a swimming pool with a capacity of 100,000 liters, and two hoses, A and B, are filling the pool simultaneously. We need to determine how long it will take to fill the pool completely when both hoses are working together. We are provided with two statements, and we need to assess whether they provide enough information to answer the question.

Let the rates at which hoses A and B fill the pool be $ r_A $ and $ r_B $ (in liters per hour). The combined rate of filling when both hoses are working together is $ r_A + r_B $, and the total time to fill the pool is $ \frac{100,000}{r_A + r_B} $.

### Statement (1):
If hose A stopped filling the pool after hoses A and B had filled $ \frac{1}{3} $ of the pool, it would take 22 hours for hose B to finish filling the remaining pool.

- In this scenario, hose A and hose B together fill $ \frac{1}{3} $ of the pool. The total amount of water filled by both hoses is $ \frac{1}{3} \times 100,000 = 33,333.33 $ liters.
- After hose A stops, hose B is left to fill the remaining $ \frac{2}{3} $ of the pool, or $ 66,666.67 $ liters.
- Since hose B alone can fill the remaining $ 66,666.67 $ liters in 22 hours, the rate of hose B is $ r_B = \frac{66,666.67}{22} = 3,030.30 $ liters per hour.

This information gives us the rate of hose B, but we still don’t know the rate of hose A or the combined rate. So, **Statement (1) alone is not sufficient**.

### Statement (2):
If hose B stopped filling the pool after hoses A and B had filled $ \frac{1}{2} $ of the pool, it would take 17 hours for hose A to finish filling the pool.

- In this scenario, hose A and hose B together fill $ \frac{1}{2} $ of the pool, or $ 50,000 $ liters.
- After hose B stops, hose A is left to fill the remaining $ 50,000 $ liters.
- Since hose A alone can fill the remaining $ 50,000 $ liters in 17 hours, the rate of hose A is $ r_A = \frac{50,000}{17} = 2,941.18 $ liters per hour.

This information gives us the rate of hose A, but we still don’t know the rate of hose B or the combined rate. So, **Statement (2) alone is not sufficient**.

### Combining Statements (1) and (2):
- From Statement (1), we know the rate of hose B: $ r_B = 3,030.30 $ liters per hour.
- From Statement (2), we know the rate of hose A: $ r_A = 2,941.18 $ liters per hour.

The combined rate of both hoses is:

\

The total time to fill the pool is:

\

Thus, **both statements together are sufficient** to determine the time it takes to fill the pool.

### Final Answer:
The answer is **C**: Both statements together are sufficient.

An empty swimming pool with a capacity of 100,000 liters is to be fill

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An empty swimming pool with a capacity of 100,000 liters is to be fill

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