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# Working together at their respective rates, two hoses fill a pool in 2

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Math Expert
Joined: 02 Sep 2009
Posts: 47033
Working together at their respective rates, two hoses fill a pool in 2 [#permalink]

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08 Aug 2017, 01:22
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Difficulty:

5% (low)

Question Stats:

86% (00:41) correct 14% (00:34) wrong based on 124 sessions

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Working together at their respective rates, two hoses fill a pool in 2 hours. If one of the hoses, working alone, could fill the pool in 3 hours, how long would it take the other hose to fill the pool alone?

A. 2 hours
B. 3 hours
C. 4 hours
D. 5 hours
E. 6 hours

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Re: Working together at their respective rates, two hoses fill a pool in 2 [#permalink]

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08 Aug 2017, 01:35
Bunuel wrote:
Working together at their respective rates, two hoses fill a pool in 2 hours. If one of the hoses, working alone, could fill the pool in 3 hours, how long would it take the other hose to fill the pool alone?

A. 2 hours
B. 3 hours
C. 4 hours
D. 5 hours
E. 6 hours

Let the hoses be $$A$$ and $$B$$.

Given $$A$$ and $$B$$ hoses together can fill a pool in $$2$$ hours.

Therefore $$1$$ hour work of $$A$$ and $$B$$ together is equal to.

$$\frac{1}{A} + \frac{1}{B} = \frac{1}{2}$$

Given $$A$$ could fill the pool in $$3$$ hours alone.

Therefore, $$A = 3$$ hours

$$\frac{1}{3} + \frac{1}{B} = \frac{1}{2}$$

$$\frac{1}{B} = \frac{1}{2} - \frac{1}{3} = \frac{3-2}{6} = \frac{1}{6}$$

$$B = 6$$ hours

Therefore $$B$$ can fill the pool alone in $$6$$ hours.

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Re: Working together at their respective rates, two hoses fill a pool in 2 [#permalink]

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08 Aug 2017, 01:37
Bunuel wrote:
Working together at their respective rates, two hoses fill a pool in 2 hours. If one of the hoses, working alone, could fill the pool in 3 hours, how long would it take the other hose to fill the pool alone?

A. 2 hours
B. 3 hours
C. 4 hours
D. 5 hours
E. 6 hours

Pool is 6 units
Hose A + Hose B = 3 units/hr
Hose A = 2 units/hr

Hose B = 1 unit/hr
Time = 6/1 = 6 hrs
E
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Re: Working together at their respective rates, two hoses fill a pool in 2 [#permalink]

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04 Dec 2017, 14:40
Hi All,

This question is a standard example of a Work Formula question (with 2 'entities' working on a job together). When this type of question has no 'quirks' to it (such as 3 or more entities or one of the entities stops working partway through the job), you can use the Work Formula to answer it:

Work = (A)(B)/(A+B) = amount of time to complete the job while working together (where A and B are the two individual times it takes to do the job).

In this prompt, we know that one of the hoses takes 3 hours to do the job alone and that the two hoses (working together) can complete the job in 2 hours....

(3)(B)/(3+B) = 2 hours
3B = (2)(3+B)
3B = 6 + 2B
B = 6 hours

Thus, it would take the second hose 6 hours to fill the pool by itself.

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Re: Working together at their respective rates, two hoses fill a pool in 2 [#permalink]

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04 Jan 2018, 11:12
Bunuel wrote:
Working together at their respective rates, two hoses fill a pool in 2 hours. If one of the hoses, working alone, could fill the pool in 3 hours, how long would it take the other hose to fill the pool alone?

A. 2 hours
B. 3 hours
C. 4 hours
D. 5 hours
E. 6 hours

We can let n = the time, in hours, it takes the other hose to fill the pool alone. Thus, the rate of that hose = 1/n. Since the rate of the known hose = 1/3 and the combined rate = 1/2, we have:

1/n + 1/3 = 1/2

Multiplying by 6n, we have:

6 + 2n = 3n

6 = n

Thus, the other hose takes 6 hours to fill the pool.

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Working together at their respective rates, two hoses fill a pool in 2 [#permalink]

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04 Jan 2018, 13:43
Bunuel wrote:
Working together at their respective rates, two hoses fill a pool in 2 hours. If one of the hoses, working alone, could fill the pool in 3 hours, how long would it take the other hose to fill the pool alone?

A. 2 hours
B. 3 hours
C. 4 hours
D. 5 hours
E. 6 hours

Since one of the hoses fills the pool in 3 hours and both the hoses
fill the pool in 2 hour, we should assume a number divisible by both
these numbers to be the total capacity of the pool. Let that be 60 units.

Let the hose which can fill the pool alone in 3 hours be hose A, so the
rate of work is 20 units/hour. Similarly, both the hoses can fill the pool
in 2 hours, and must fill 30 units/hour.

Hence, the other hose must be filling the pool at the rate of 10 units/hr

Therefore, the time taken to fill the entire pool is $$\frac{60}{10}$$(6 hours - Option E)
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Re: Working together at their respective rates, two hoses fill a pool in 2 [#permalink]

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10 Jan 2018, 08:26
Top Contributor
Bunuel wrote:
Working together at their respective rates, two hoses fill a pool in 2 hours. If one of the hoses, working alone, could fill the pool in 3 hours, how long would it take the other hose to fill the pool alone?

A. 2 hours
B. 3 hours
C. 4 hours
D. 5 hours
E. 6 hours

Another approach is to assign a nice value to the job.
In this case, we need a value that works well with the given information (2 hours and 3 hours).
So, let's say the job consists of filling a pool containing 6 liters of water

One of the hoses, working alone, takes 3 hours to fill the pool
We'll call this hose A.
Let A = the rate of work of this hose
If it takes 3 hours for this hose to fill a 6-liter pool, then....
A = 6/3 = 2 liters per hour (since rate = output/time)

Working together at their respective rates, two hoses fill a pool in 2 hours.
Let B = the rate of work of the other hose
So, the COMBINED rate = A+B
If it takes 2 hours for the combined hoses to fill a 6-liter pool then....
A+B = 6/2 = 3 liters per hour (since rate = output/time)

So, if A = 2 liters per hour, and A+B = 3 liters per hour
Then we can see that B = 1 liter per hour

How long would it take the other hose (hose B) to fill the pool alone?
Time = output/rate = 6/1 = 6 hours

Cheers,
Brent
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Re: Working together at their respective rates, two hoses fill a pool in 2 [#permalink]

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10 Jan 2018, 09:03
Bunuel wrote:
Working together at their respective rates, two hoses fill a pool in 2 hours. If one of the hoses, working alone, could fill the pool in 3 hours, how long would it take the other hose to fill the pool alone?

A. 2 hours
B. 3 hours
C. 4 hours
D. 5 hours
E. 6 hours

Let the total capacity of the pool be 6 units

Efficiency of A + B = 3 units/hr
Efficiency of B = 2 units/hr

So, Efficiency of A = 1 unit/hr

Thus, time required to fill the pool alone is 6 hours, answer will be (E)
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Re: Working together at their respective rates, two hoses fill a pool in 2   [#permalink] 10 Jan 2018, 09:03
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