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# A pump started filling an empty pool with water and continue

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Manager
Joined: 10 Oct 2008
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A pump started filling an empty pool with water and continue  [#permalink]

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Updated on: 11 Apr 2014, 03:29
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Difficulty:

15% (low)

Question Stats:

80% (02:00) correct 20% (02:28) wrong based on 415 sessions

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A pump started filling an empty pool with water and continued at a constant rate until the pool was full. At noon the pool was 1/3 full, and $$1\frac{1}{4}$$ hours later it was 3/4 full. What was the total number of hours that it took the pump to fill the pool?

A. $$2\frac{1}{3}$$
B. $$2\frac{2}{3}$$
C. 3
D. $$3\frac{1}{2}$$
E. $$3\frac{2}{3}$$

Originally posted by Jcpenny on 20 Nov 2008, 11:30.
Last edited by Bunuel on 11 Apr 2014, 03:29, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
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Re: A pump started filling an empty pool with water and  [#permalink]

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10 Apr 2014, 20:13
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Jcpenny wrote:
A pump started filling an empty pool with water and continued at
a constant rate until the pool was full. At noon the pool was 1/3 full,
and 1+1/4 hours later it was 3/4 full. What was the total number of
hours that it took the pump to fill the pool?
A. 2+1/3 B. 2+2/3 C. 3
D. 3+1/2 E. 3+2/3

The time elapsed between 1/3 full pool and 3/4 full pool is 5/4 hrs. This means 3/4 - 1/3 = 5/12 of the pool was filled in 5/4 hrs.

Again, (5/12)th of the pool will be filled in 5/4 hrs

1 pool will be filled in $$\frac{5/4}{5/12} * 1 = 3$$ hrs
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Karishma
Veritas Prep GMAT Instructor

##### General Discussion
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Joined: 14 Aug 2007
Posts: 635

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20 Nov 2008, 23:18
1
Jcpenny wrote:
A pump started filling an empty pool with water and continued at
a constant rate until the pool was full. At noon the pool was 1/3 full,
and 1+1/4 hours later it was 3/4 full. What was the total number of
hours that it took the pump to fill the pool?
A. 2+1/3 B. 2+2/3 C. 3
D. 3+1/2 E. 3+2/3

in 1+1/4 =5/4 hrs the pump filled 3/4-1/3 = 5/12th of the pool
in 1 hr it fills 1/3 of the pool
so in 3 hrs it will fill the entire pool.
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Joined: 02 Dec 2012
Posts: 33
GMAT Date: 01-01-2014

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10 Apr 2014, 17:22
1
alpha_plus_gamma wrote:
Jcpenny wrote:
A pump started filling an empty pool with water and continued at
a constant rate until the pool was full. At noon the pool was 1/3 full,
and 1+1/4 hours later it was 3/4 full. What was the total number of
hours that it took the pump to fill the pool?
A. 2+1/3 B. 2+2/3 C. 3
D. 3+1/2 E. 3+2/3

in 1+1/4 =5/4 hrs the pump filled 3/4-1/3 = 5/12th of the pool
in 1 hr it fills 1/3 of the pool
so in 3 hrs it will fill the entire pool.

I was with you up until 5/12th of the pool. How did you get the in 1 hour it fills 1/3 of the poor?
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A pump started filling an empty pool with water and continue  [#permalink]

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02 Jun 2015, 07:04
2
Jcpenny wrote:
A pump started filling an empty pool with water and continued at a constant rate until the pool was full. At noon the pool was 1/3 full, and $$1\frac{1}{4}$$ hours later it was 3/4 full. What was the total number of hours that it took the pump to fill the pool?

A. $$2\frac{1}{3}$$
B. $$2\frac{2}{3}$$
C. 3
D. $$3\frac{1}{2}$$
E. $$3\frac{2}{3}$$

Taking a smart number.
Let the capacity of the pool be 12 Liters

At 12 PM = $$\frac{1}{3}*12$$ = 4 Liters of water was in the pool.
After $$1\frac{1}{4}$$ Hours i.e. at 13:15 Hrs = $$\frac{3}{4}*12$$ = 9 liters of water was in the pool.

So in 75 mins the pump fills 9-4 = 5 liters of water in the pool.

setting up ratio and proportion

$$\frac{X}{75}=\frac{12}{5}$$
$$X = 180 mins = 3 Hours$$

SVP
Joined: 06 Nov 2014
Posts: 1877
Re: A pump started filling an empty pool with water and continue  [#permalink]

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02 Jun 2015, 08:54
2
1
A pump started filling an empty pool with water and continued at a constant rate until the pool was full. At noon the pool was 1/3 full, and 1 1/4 hours later it was 3/4 full. What was the total number of hours that it took the pump to fill the pool?

(3/4) - (1/3) = 5/12. 5/12 of the pool was full in 1 1/4 hours time (5/4 hours). To determine a rate of filling we divide how much is full by the time. That is (5/12) ÷ (5/4) = 1/3. This means it fills a pool in 3 hours.

A. 2 1/3
B. 2 2/3
C. 3
D. 3 1/2
E. 3 2/3
Current Student
Joined: 08 Jun 2013
Posts: 33
Re: A pump started filling an empty pool with water and continue  [#permalink]

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24 Sep 2016, 05:14
at noon or 12:00PM it is filled 1/3 of total, say x = 1/3x
1hour 15 mins later it is 3/4x filled
so amount it filled in 75mins = (3/4)x - (1/3)x
=> 15*12 mins => 3 hours
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Re: A pump started filling an empty pool with water and continue  [#permalink]

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16 Mar 2017, 10:46
OptimusPrepJanielle wrote:
A pump started filling an empty pool with water and continued at a constant rate until the pool was full. At noon the pool was 1/3 full, and 1 1/4 hours later it was 3/4 full. What was the total number of hours that it took the pump to fill the pool?

(3/4) - (1/3) = 5/12. 5/12 of the pool was full in 1 1/4 hours time (5/4 hours). To determine a rate of filling we divide how much is full by the time. That is (5/12) ÷ (5/4) = 1/3. This means it fills a pool in 3 hours.

A. 2 1/3
B. 2 2/3
C. 3
D. 3 1/2
E. 3 2/3

I got as far as finding 5/12- though where are you getting 3 hours? Is it the reciprocal of 1/3?
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Re: A pump started filling an empty pool with water and continue  [#permalink]

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17 Mar 2017, 03:34
let the total volume be x and rate of flow be r

3x/4 - x/3 = r *5/4
or 5x/12 = r*5/4
or x = r*3

therefre in three hours, the pool will be filled
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Re: A pump started filling an empty pool with water and continue  [#permalink]

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21 Mar 2017, 06:22
2
Jcpenny wrote:
A pump started filling an empty pool with water and continued at a constant rate until the pool was full. At noon the pool was 1/3 full, and $$1\frac{1}{4}$$ hours later it was 3/4 full. What was the total number of hours that it took the pump to fill the pool?

A. $$2\frac{1}{3}$$
B. $$2\frac{2}{3}$$
C. 3
D. $$3\frac{1}{2}$$
E. $$3\frac{2}{3}$$

Since it took 1¼ = 5/4 hours to fill 3/4 - 1/3 = 9/12 - 4/12 = 5/12 of the pool, we can let x = the number of hours to fill the pool and create a proportion to determine how long it will take to fill the entire pool.

(5/4)/(5/12) = x/1

5/4 = 5x/12

60 = 20x

x = 3

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Re: A pump started filling an empty pool with water and continue  [#permalink]

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20 Jan 2018, 16:49
VeritasPrepKarishma wrote:
Jcpenny wrote:
A pump started filling an empty pool with water and continued at
a constant rate until the pool was full. At noon the pool was 1/3 full,
and 1+1/4 hours later it was 3/4 full. What was the total number of
hours that it took the pump to fill the pool?
A. 2+1/3 B. 2+2/3 C. 3
D. 3+1/2 E. 3+2/3

The time elapsed between 1/3 full pool and 3/4 full pool is 5/4 hrs. This means 3/4 - 1/3 = 5/12 of the pool was filled in 5/4 hrs.

Again, (5/12)th of the pool will be filled in 5/4 hrs

1 pool will be filled in $$\frac{5/4}{5/12} * 1 = 3$$ hrs

Hi Karishma,

I was able to follow till the last portion. Can you clarify why we are able to divide the time by rate to figure out how long it will take to fill 1 pool? I was able to solve this correctly however I am looking for a faster way to solve these type of problems.

Thanks!
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Re: A pump started filling an empty pool with water and continue  [#permalink]

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02 Jan 2019, 12:04
We have only one variable (volume of the pool) so let us assume the volume of the pool is 12 liters

At noon, the pool is 4 L (1/3 x 12 L) full, we do not know the time it took to fill 4 L of the pool at this point

At 1:15 pm (75 mins later), the pool is 9 L (3/4 x 12 L) full =====> Rate = (9 - 4) L/75 mins = 1/15 L/min

Therefore, it took 60 mins (4 L x 15 L/min) to fill the 4 L at noon

Time it took to fill the remaining 3 L (remember we assumed the pool is 12 L?) is 45 mins (3 L * 15 L/min)

Therefore, the total time it took to fill the pool = 60 + 75 + 45 = 180 minutes = 3 hours (Answer choice C)

Jcpenny wrote:
A pump started filling an empty pool with water and continued at a constant rate until the pool was full. At noon the pool was 1/3 full, and $$1\frac{1}{4}$$ hours later it was 3/4 full. What was the total number of hours that it took the pump to fill the pool?

A. $$2\frac{1}{3}$$
B. $$2\frac{2}{3}$$
C. 3
D. $$3\frac{1}{2}$$
E. $$3\frac{2}{3}$$
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Joined: 09 Aug 2018
Posts: 12
Re: A pump started filling an empty pool with water and continue  [#permalink]

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29 Mar 2019, 08:15

Hello - Why we are able to divide the time by rate to figure out how long it will take to fill 1 pool? "(5/4)/(5/12)∗1=3 hrs"
I thought the formula to calculate the time is: Time = Work/Rate but that gives me 1/3. Thank you very much in advance!
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Re: A pump started filling an empty pool with water and continue  [#permalink]

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30 Mar 2019, 23:36
lstsch wrote:

Hello - Why we are able to divide the time by rate to figure out how long it will take to fill 1 pool? "(5/4)/(5/12)∗1=3 hrs"
I thought the formula to calculate the time is: Time = Work/Rate but that gives me 1/3. Thank you very much in advance!

"The time elapsed between 1/3 full pool and 3/4 full pool is 5/4 hrs. This means 3/4 - 1/3 = 5/12 of the pool was filled in 5/4 hrs.

Again, (5/12)th of the pool will be filled in 5/4 hrs"

I am guessing you understand this part. Rest is all application the formula Work = Rate*Time only. Here is how:

(5/12)th of the pool (this is amount of work done - amount of pool filled) will be filled in (5/4) hrs (this is time taken for this work done)

So constant RATE of filling pool = Work / Time = (5/12) / (5/4)

Now, this is the constant rate. We want the time taken to fill 1 pool (work to be done is 1)

Time taken to fill 1 pool = Work / Rate = 1 / ((5/12) / (5/4) = (5/4) / (5/12)

Note what is the work done and time taken in each case. You have been given time taken (5/4 hrs) for certain amount of work (5/12th pool) first. You use this to get the rate of filling. Then you use the rate to find the time taken to do a different amount of work (1 pool). So you apply the formula twice.

In my explanation, I have simply used the direct variation between work and time to get the answer. Knowing that rate is constant, I say:

A amount of work is done in time T.
B amount of work will be done in (T/A)*B

e.g. 1/2 work is done in 2 hrs
1 full work will be done in 2/(1/2) * 1 = 4 hrs
If work doubles, time taken doubles too.
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Re: A pump started filling an empty pool with water and continue   [#permalink] 30 Mar 2019, 23:36
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