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

Question

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

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

EMPOWERgmatRichC · Accepted Answer

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.

Final Answer:  B

GMAT assassins aren't born, they're made,
Rich

Nunuboy1994 · Answer

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.

CounterSniper · Answer

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

sagnik242 · Answer

But how do we know when we have to convert minutes to hours? What is an example of a more twisted problem?

EMPOWERgmatRichC · Answer

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.

GMAT assassins aren't born, they're made,
Rich

infinitemac · Answer

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!

EMPOWERgmatRichC · Answer

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.

GMAT assassins aren't born, they're made,
Rich

Suryangshu · Answer

20*30/(20+30)= 12 mins

BrentGMATPrepNow · Answer

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

Cheers.
Brent

JeffTargetTestPrep · Answer

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

GMATinsight · Answer

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

Abhishek009 · Answer

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)

gadhiakhushboo · Answer

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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ManifestDreamMBA · Answer

10-15 sec solution

Think about it this way, if 2 large hoses are used, it will be take (20/2) = 10 mins and if 2 small hoses are used, it will take (30/2) = 15mins. Therefore if a combination of these 2 hoses are used, time will be between 10 and 15mins and there's only option B which satisfies this.

sriharsha4444 · Answer

if both took 20 mins each, together it would take 10 mins
if both took 30 mins each, together it would take 15 mins

together it has to be between 10 and 15 mins. B is the only option that satisfies this

BadukMagician · Answer

Fun if we use 2 large houses our avg time would be 10, if we use 2 small hoses our average time would be 15 so the answer has to be between 10 and 15, thus answer b 12

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

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