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At a constant Rate of flow, it takes 20 minutes to fill a swimming poo

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At a constant Rate of flow, it takes 20 minutes to fill a swimming poo  [#permalink]

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New post 23 Dec 2015, 12:12
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At a constant Rate of flow, it takes 20 minutes to fill a swimming pool if a large hose is used and 30 minutes if a small hose is Used. At these constant rates, how many minutes will it take to fill the pool when both hoses are used simultaneously?


A. 10
B. 12
C. 15
D. 25
E. 50

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Re: At a constant Rate of flow, it takes 20 minutes to fill a swimming poo  [#permalink]

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New post 26 Dec 2015, 09:10
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Hi All,

This is a standard Work Formula question (2 or more 'entities' that work on a task together). When there are just 2 entities and there are no 'twists' to the question, we can use the Work Formula to get to the correct answer.

Work = (A)(B)/(A+B) where A and B are the individual times needed to complete the task.

We're told that two hoses take 20 minutes and 30 minutes, respectively, to fill a pool. We're asked how long it takes the two hoses, working together, to fill the pool.

(20)(30)/(20+30) = 600/50 = 12 minutes to fill the pool.

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Re: At a constant Rate of flow, it takes 20 minutes to fill a swimming poo  [#permalink]

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New post 24 Dec 2015, 02:42
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can be done in a few ways.

The std way

time taken to fill the pool by Large Hose =20 minutes =L or 1/L=1/20 similarly 1/S=1/30
simultaneously it will take 1/L+1/S=1/20+1/30=5/60=12 minutes

efficiency way (not necessarily the efficient way)

let l and s denote efficiency of large and small hose
efficiency = 100/time take to fill the pool=100/30=3.33% for smaller hose
similarly 100/20=5% for the larger hose
working together 8.33% per minute
time taken = 100/8.33 ===12.0048 ~ 12 minutes
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Re: At a constant Rate of flow, it takes 20 minutes to fill a swimming poo  [#permalink]

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New post 12 Jan 2016, 18:51
EMPOWERgmatRichC wrote:
Hi All,

This is a standard Work Formula question (2 or more 'entities' that work on a task together). When there are just 2 entities and there are no 'twists' to the question, we can use the Work Formula to get to the correct answer.

Work = (A)(B)/(A+B) where A and B are the individual times needed to complete the task.

We're told that two hoses take 20 minutes and 30 minutes, respectively, to fill a pool. We're asked how long it takes the two hoses, working together, to fill the pool.

(20)(30)/(20+30) = 600/50 = 12 minutes to fill the pool.

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But how do we know when we have to convert minutes to hours? What is an example of a more twisted problem?
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Re: At a constant Rate of flow, it takes 20 minutes to fill a swimming poo  [#permalink]

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New post 12 Jan 2016, 19:19
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HI sagnik242,

The simple answer to your question is that we have to follow whatever 'instructions' we're given in the prompt. Here, we're given the two rates (time to fill the pool) in terms of 'minutes' and we're asked for an answer in 'minutes.' As such, there are no 'twists' or extra steps (and converting minutes to hours would like make all the work take longer).

If you're looking for more-complex Work questions, then you can search for them in the Quant Forums here.

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Re: At a constant Rate of flow, it takes 20 minutes to fill a swimming poo  [#permalink]

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New post 15 Mar 2017, 23:25
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RSOHAL wrote:
At a constant Rate of flow, it takes 20 minutes to fill a swimming pool if a large hose is used and 30 minutes if a small hose is Used. At these constant rates, how many minutes will it take to fill the pool when both hoses are used simultaneously?


A. 10
B. 12
C. 15
D. 25
E. 50


In order to solve this question we need to know the combined work rate of the small hose and large hose.

Small Hose= 1 job / 20 mins

Large Hose= 1 job/ 30 mins

We must set the denominators equal and add the two fractions

3 jobs/ 60 mins + 2 jobs/ 60 mins = 5 jobs / 60 mins

Therefore

1 job / 12 mins- 1 job is done in 12 minutes at this combined work rate.
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At a constant Rate of flow, it takes 20 minutes to fill a swimming poo  [#permalink]

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New post 06 May 2017, 16:48
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I had approached the question by picking numbers, but not sure if this is correct - can someone please verify if I what did below is correct or not?

Since in the question, they don't tell us the quantity to fill the pool with each hose, I just chose 60 liters as an estimate, therefore:

For large hose: 60L /20 min = 3L in 1 min
For small hose: 60L/30 min = 2L in 1 min

Combined rates: 3L + 2L = 5L in 1 min together, so if we wanted to find how much it would take to fill up to the original 60L, that would mean you multiplied 5L by 12, therefore, 60 L would fill up in 12 min with the two hoses. Does this make sense or is the approach of picking numbers incorrect?

Thanks!
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Re: At a constant Rate of flow, it takes 20 minutes to fill a swimming poo  [#permalink]

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New post 07 May 2017, 10:38
Hi infinitemac,

YES - your approach (TESTing VALUES) works just fine on this question. Since the prompt tells us nothing about the actual rates of the two hoses nor about the volume of the swimming pool, you can choose whatever values you like - as long as they properly account for the times that it takes the two hoses to fill the pool individually.

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Re: At a constant Rate of flow, it takes 20 minutes to fill a swimming poo  [#permalink]

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New post 13 Aug 2017, 23:23
20*30/(20+30)= 12 mins
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Re: At a constant Rate of flow, it takes 20 minutes to fill a swimming poo  [#permalink]

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New post 30 Aug 2018, 06:29
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RSOHAL wrote:
At a constant Rate of flow, it takes 20 minutes to fill a swimming pool if a large hose is used and 30 minutes if a small hose is Used. At these constant rates, how many minutes will it take to fill the pool when both hoses are used simultaneously?


A. 10
B. 12
C. 15
D. 25
E. 50


Let's assign a nice value to the volume of the pool. We want a volume that works well with the given information (20 minutes and 30 minutes).
So, let's say the pool has a total volume of 60 gallons

It takes 20 minutes to fill a swimming pool with a LARGE hose
In other words, the LARGE hose can pump 60 gallons of water in 20 minutes
So, the RATE of the large hose = 3 gallons per minute

It takes 30 minutes to fill a swimming pool with a SMALL hose
In other words, the SMALL hose can pump 60 gallons of water in 30 minutes
So, the RATE of the small hose = 2 gallons per minute

So, the COMBINED rate of BOTH pumps = 3 gallons per minute + 2 gallons per minute = 5 gallons per minute

How many minutes will it take to fill the pool when both hoses are used simultaneously?
We need to pump 60 gallons of water, and the combined rate is 5 gallons per minute
Time = output/rate
= 60/5
= 12 minutes

Answer: B

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Re: At a constant Rate of flow, it takes 20 minutes to fill a swimming poo  [#permalink]

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New post 04 Sep 2018, 03:54
RSOHAL wrote:
At a constant Rate of flow, it takes 20 minutes to fill a swimming pool if a large hose is used and 30 minutes if a small hose is Used. At these constant rates, how many minutes will it take to fill the pool when both hoses are used simultaneously?


A. 10
B. 12
C. 15
D. 25
E. 50


We are given that the large hose takes 20 minutes to fill a swimming pool and that the small hose takes 30 minutes to fill the same swimming pool.

Since rate = work/time, the rate of the large hose is 1/20 and the rate of the small hose is 1/30.

We need to determine the number of minutes, when working simultaneously, it would take both hoses to fill the swimming pool. To solve, we can use the combined worker formula.

work of the large hose + work of the small hose = total work

Since the pool is being filled, the total work completed is 1 job. We can also let the time worked, in minutes, for both hoses, equal the variable t. Using the formula work = rate x time, we express the work of each hose as follows:

work of the large hose = (1/20)t

work of the small hose = (1/30)t

Lastly, we can determine t:

work of the small hose + work of the large hose = 1

(1/20)t + (1/30)t = 1

(3/60)t + (2/60)t = 1

(5/60)t = 1

t = 1/(5/60)

t = 60/5

t = 12

Alternate Solution:

In one minute, the larger hose can fill 1/20 of the pool, and the smaller hose can fill 1/30 of the pool. If they are used simultaneously, they fill 1/20 + 1/30 = 5/60 = 1/12 of the pool in one minute. If they fill 1/12 of the pool in one minute, they will fill 12/12 of the pool in 12 minutes.

Answer: B
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Re: At a constant Rate of flow, it takes 20 minutes to fill a swimming poo  [#permalink]

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New post 04 Sep 2018, 04:18
RSOHAL wrote:
At a constant Rate of flow, it takes 20 minutes to fill a swimming pool if a large hose is used and 30 minutes if a small hose is Used. At these constant rates, how many minutes will it take to fill the pool when both hoses are used simultaneously?


A. 10
B. 12
C. 15
D. 25
E. 50


CONCEPT: \(\frac{(Machine_Power * Time)}{Work} = Constant\)
i.e. \(\frac{(M_1 * T_1)}{W_1} = \frac{(M_2 * T_2)}{W_2}\)

20L = 30S
i.e. L = 1.5S
Both Hoses = L+S = 1.5S+S = 2.5S

i.e. \(\frac{(S * 30)}{1} = \frac{(2.5S * T_2)}{1}\)

i.e. \(T_2 = 30/2.5 = 12\)

Answer: option B
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Re: At a constant Rate of flow, it takes 20 minutes to fill a swimming poo  [#permalink]

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New post 04 Sep 2018, 07:26
RSOHAL wrote:
At a constant Rate of flow, it takes 20 minutes to fill a swimming pool if a large hose is used and 30 minutes if a small hose is Used. At these constant rates, how many minutes will it take to fill the pool when both hoses are used simultaneously?


A. 10
B. 12
C. 15
D. 25
E. 50

Let the capacity of the swimming pool be 60 units

So, Efficiency of the Large hose is 3 units/min & The efficiency of the Small hose is 2 units/min

So, Time required to completely fill the Pool when both the hose's are in operation is 60/(3 + 2) = 12 Min, Answer must be (B)
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Re: At a constant Rate of flow, it takes 20 minutes to fill a swimming poo  [#permalink]

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New post 23 Dec 2018, 07:36
Volume filled by hose A in 1 min = 1/20
Volume filled by hose B in 1 min = 1/30
Both (A+B) = 1/20+1/30 = 5/60 = 1/12
Thus, 12 minutes.
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Re: At a constant Rate of flow, it takes 20 minutes to fill a swimming poo &nbs [#permalink] 23 Dec 2018, 07:36
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At a constant Rate of flow, it takes 20 minutes to fill a swimming poo

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