A pump started filling an empty pool with water and continue

Question

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. \(3\frac{2}{3}\)

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

KarishmaB · Accepted Answer

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

Ashishmathew01081987 · Answer

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

Answer is C

BrentGMATPrepNow · Answer

For this type of question, I like to assign a "nice value" to the job.

In this case we're looking for a number that works well with 1/3, 3/4 and even 1 1/4
So, let's say the pool has a capacity of   60   liters.

At noon the pool was 1/3 full, . . .   
1/3 of   60   liters = 20 liters
So, at 12:00pm, the pool contained 20 liters of water

. . . and 1 1/4 hours later it was 3/4 full.   
1 1/4 hours = 1.25 hours = 75 minutes.
3/4 of   60   liters = 45 liters
So, at 1:15pm, the pool contained 45 liters of water

What was the total number of hours that it took the pump to fill the pool?  
45 liters - 20 liters = 25 liters
So, in 1.25 hours, 25 liters of water was added to the pool

Rate = output/time 
So, the rate at which water is added to the pool = (25 liters)/(1.25 hours) =   20 liters per hour

Time = output/rate 
So, at a rate of   20 liters per hour  , the time it takes to fill the   60   liter pool =   60  /  20 liters   =  3 hours

Answer: C

alpha_plus_gamma · Answer

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.

nevermoreflow · Answer

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?

OptimusPrepJanielle · Answer

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. \(3\frac{2}{3}\)

(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

urfrndniks · Answer

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

Nunuboy1994 · Answer

I got as far as finding 5/12- though where are you getting 3 hours? Is it the reciprocal of 1/3?

KrishnakumarKA1 · Answer

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

JeffTargetTestPrep · Answer

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

Answer: C

john133 · Answer

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!

bebs · Answer

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 )

lstsch · Answer

chetan2u   VeritasKarishma

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!

KarishmaB · Answer

"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.

Kinshook · Answer

Given: 
1. A pump started filling an empty pool with water and continued at a constant rate until the pool was full. 
2. At noon the pool was 1/3 full, and  1\frac{1}{4}  hours later it was 3/4 full.

Asked: What was the total number of hours that it took the pump to fill the pool?

At 1200 hrs, the pool was 1/3 full
 1\frac{1}{4}  hours later it was 3/4 full.

In 5/4 hours, pump fills = 3/4 - 1/3 = (9-4)/12 = 5/12 of the pool
In 1 hour, pump fills = 5*4/5*12 = 1/3 of the pool

Number of hours required to fill the pool = 3 hours

IMO C

Archit3110 · Answer

let total capacity by 12 
noon filling done is 4 units
1.25 hrs later 9 units
rate per hour is 
(9-4) ; 5 units

time 5/4 hrs
rate 5*4/5 ; 4 units per hr

3 units will be filled in 3/4 ; .75 hrs
total time 1+.25+.75 
3 hrs
OPTION C

malfoy · Answer

No pen method, 
Pool was  \frac{1}{3}  filled at 12:00 PM and  1\frac{1}{4}  hours later i.e.  \frac{5}{4}  hours => 1 hr 15 mins later it was  \frac{3}{4}  full.
 \frac{1}{3}  =  \frac{4}{12}  and  \frac{3}{4}  =  \frac{9}{12}

=>  \frac{5}{12}  in  \frac{5}{4} hr 
=> 1 (whole pool would be filled) in 3 hrs (D)

Leon685 · Answer

Just determine the rate

work = 3/4 - 1/3 = 5/12
time = 5/4

w = rt
5/12 = r*5/4 | * 4/5
r = 1/3
--> 1 work (fill the pool) in 3 hours

Answer C

A pump started filling an empty pool with water and continue

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