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

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An empty swimming pool with a capacity of 100,000 liters is [#permalink] New post 14 Aug 2009, 21:08
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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 ½ of the pool, it would take 17 hours for hose A to finish filling the pool.
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Re: Rates [#permalink] New post 14 Aug 2009, 21:37
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
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Re: Rates [#permalink] New post 15 Aug 2009, 12:52
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 :)
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Re: Rates [#permalink] New post 03 Oct 2009, 19:20
Economist wrote:
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 :)


Yep absolutely. It's a great trap though and I fell into it.
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Re: Rates [#permalink] New post 03 Oct 2009, 23:14
bipolarbear wrote:
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 ½ of the pool, it would take 17 hours for hose A to finish filling the pool.



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.
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Re: Rates [#permalink] New post 18 Mar 2011, 08:48
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.
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Re: Rates [#permalink] New post 18 Mar 2011, 11:31
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).
Re: Rates   [#permalink] 18 Mar 2011, 11:31
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