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

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Manager
Joined: 10 Oct 2008
Posts: 56
A pump started filling an empty pool with water and continue [#permalink]

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20 Nov 2008, 10:30
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83% (01:33) correct 17% (02:11) wrong based on 343 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. $$3\frac{2}{3}$$
[Reveal] Spoiler: OA

Last edited by Bunuel on 11 Apr 2014, 02:29, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
Director
Joined: 14 Aug 2007
Posts: 726

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20 Nov 2008, 22:18
1
KUDOS
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.
Intern
Joined: 02 Dec 2012
Posts: 33
GMAT Date: 01-01-2014

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10 Apr 2014, 16:22
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?
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7960
Location: Pune, India
Re: A pump started filling an empty pool with water and [#permalink]

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10 Apr 2014, 19:13
Expert's post
2
This post was
BOOKMARKED
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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Manager
Status: I am not a product of my circumstances. I am a product of my decisions
Joined: 20 Jan 2013
Posts: 130
Location: India
Concentration: Operations, General Management
GPA: 3.92
WE: Operations (Energy and Utilities)
A pump started filling an empty pool with water and continue [#permalink]

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02 Jun 2015, 06:04
1
KUDOS
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: 1904
Re: A pump started filling an empty pool with water and continue [#permalink]

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02 Jun 2015, 07:54
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This post was
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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 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
Intern
Joined: 08 Jun 2013
Posts: 35
Re: A pump started filling an empty pool with water and continue [#permalink]

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24 Sep 2016, 04:14
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
C is the answer
Director
Joined: 12 Nov 2016
Posts: 790
Re: A pump started filling an empty pool with water and continue [#permalink]

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16 Mar 2017, 09:46
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?
Senior Manager
Joined: 05 Jan 2017
Posts: 434
Location: India
Re: A pump started filling an empty pool with water and continue [#permalink]

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17 Mar 2017, 02:34
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
Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2016
Re: A pump started filling an empty pool with water and continue [#permalink]

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21 Mar 2017, 05:22
1
KUDOS
Expert's post
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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Intern
Joined: 30 Jul 2017
Posts: 1
Re: A pump started filling an empty pool with water and continue [#permalink]

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20 Jan 2018, 15:49
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!
Re: A pump started filling an empty pool with water and continue   [#permalink] 20 Jan 2018, 15:49
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# A pump started filling an empty pool with water and continue

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