An empty pool being filled with water at a constant rate : GMAT Problem Solving (PS)
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# An empty pool being filled with water at a constant rate

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An empty pool being filled with water at a constant rate [#permalink]

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20 Dec 2012, 04:53
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An empty pool being filled with water at a constant rate takes 8 hours to fill to 3/5 of its capacity. How much more time will it take to finish filling the pool?

(A) 5 hr 30 min
(B) 5 hr 20 min
(C) 4 hr 48 min
(D) 3 hr 12 min
(E) 2 hr 40 min
[Reveal] Spoiler: OA
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Re: An empty pool being filled with water at a constant rate [#permalink]

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20 Dec 2012, 04:56
Walkabout wrote:
An empty pool being filled with water at a constant rate takes 8 hours to fill to 3/5 of its capacity. How much more time will it take to finish filling the pool?

(A) 5 hr 30 min
(B) 5 hr 20 min
(C) 4 hr 48 min
(D) 3 hr 12 min
(E) 2 hr 40 min

As pool is filled to 3/5 of its capacity then 2/5 of its capacity is left to fill.

Since it takes 8 hours to fill 3/5 of the pool, then to fill 2/5 of the pool it will take 8/(3/5)*2/5 = 16/3 hours = 5 hours 20 minutes (because if t is the time needed to fill the pool then t*3/5=8 --> t=8*5/3 hours --> to fill 2/5 of the pool 8*5/3*2/5=16/3 hours will be needed).

Or plug values: take the capacity of the pool to be 5 liters --> 3/5 of the pool or 3 liters is filled in 8 hours, which gives the rate of 3/8 liters per hour --> remaining 2 liters will require: time = job/rate = 2/(3/8) = 16/3 hours = 5 hours 20 minutes.

Answer: B.
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Re: An empty pool being filled with water at a constant rate [#permalink]

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26 Jan 2013, 04:33
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I tried using just ratios to solve this (because rate is constant):

8Hrs to fill 3/5 tank i.e 0.6 of the tank
X hrs to fill 2/5 tank i.e 0.4 of the tank

=> 8/0.6 = X/0.4
=> X=3.2/0.6 = 32/6 = 16/3 = 5.33hrs i.e 5hr20min
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28 Jan 2013, 13:28
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Hey,
Is'nt 16/3 = 5.3 ~ . This might be silly, but i chose 5 hours 30 mins . I don't want to make this mistake again, kindly help me

Thanks
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28 Jan 2013, 14:11
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30 minutes/60 minutes=.5, so 5 and a half hours would be 5.5, not 5.33.
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21 May 2015, 03:55
Let the total amount of water eq l

then rate : ( 3/5 * l ) / 8 = 3/40 * l

So time required to fill the full tank = l / ( (3/40) * l ) = 40/3

So time required to fill the remaining section = ( 40/3 - 8 ) hrs = 16/3 hrs = 5 1/3 hrs = 5 hr 20 min
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Re: An empty pool being filled with water at a constant rate takes 8 hours [#permalink]

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29 May 2015, 20:03
As per what I did,

8 Hours - 3/5 of capacity
? Time - to fill remaining - 2/5 of capacity.

But the answer I am getting is incorrect. Could someone share the appropriate process to work on this?
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Re: An empty pool being filled with water at a constant rate takes 8 hours [#permalink]

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29 May 2015, 20:08
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Hi Pretz,

There are a couple of different ways to approach the math in this question. It looks like you started to set up a ratio, but didn't complete the work. Here's one way to go about it:

Since it takes 8 hours to fill 3/5 of the pool and X hours to fill 2/5 of the pool.....

8/X = (3/5)/(2/5)

Since both fractions are "over 5", we can multiply those 5s out (by multiplying the numerator and denominator by 5)....

8/X = 3/2

Now we can cross-multiply and solve for X....

16 = 3X
16/3 = X
5 1/3 hours = X

5 1/3 hours = 5 hours 20 minutes

Final Answer:
[Reveal] Spoiler:
B

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# Special Offer: Save $75 + GMAT Club Tests 60-point improvement guarantee www.empowergmat.com/ ***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*********************** Manager Joined: 21 Feb 2012 Posts: 61 Followers: 1 Kudos [?]: 50 [0], given: 63 An empty pool being filled with water at a constant rate takes 8 hours [#permalink] ### Show Tags 29 May 2015, 20:46 Pretz wrote: As per what I did, 8 Hours - 3/5 of capacity ? Time - to fill remaining - 2/5 of capacity. But the answer I am getting is incorrect. Could someone share the appropriate process to work on this? Hello there Pretz I think your approach is fine. $$8$$ $$hours$$ ----- $$\frac{3}{5}$$ multiply by $$\frac{5}{3}$$ on both sides $$8*\frac{5}{3}$$ $$hours$$ ----- $$\frac{3}{5} *\frac{5}{3}$$ $$\frac{40}{3}$$ $$hours$$ ----- $$1$$ So it takes $$\frac{40}{3}$$ $$hours$$ to fill the tank The additional time required to fill $$\frac{2}{3}$$rd of the tank will be $$\frac{40}{3} - 8$$ $$hours$$ $$\frac{16}{3}$$ $$hours$$ $$5 \frac{1}{3}$$ $$hours$$ $$5$$ $$hours$$ $$20$$ $$minutes$$ I hope that explains it _________________ Regards J Do consider a Kudos if you find the post useful GMAT Tutor Joined: 24 Jun 2008 Posts: 1183 Followers: 422 Kudos [?]: 1512 [1] , given: 4 Re: An empty pool being filled with water at a constant rate takes 8 hours [#permalink] ### Show Tags 29 May 2015, 20:53 1 This post received KUDOS Expert's post If it takes 8 hours to fill 3/5 of the pool, then it takes 8/3 hours to fill 1/5 of the pool, and it thus takes 16/3 hours to fill 2/5 of the pool, which is what we need to do. _________________ GMAT Tutor in Toronto If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com Intern Joined: 30 Jul 2013 Posts: 41 Concentration: Technology, General Management GMAT Date: 07-03-2015 GPA: 3.8 WE: Information Technology (Computer Software) Followers: 0 Kudos [?]: 12 [0], given: 27 Re: An empty pool being filled with water at a constant rate takes 8 hours [#permalink] ### Show Tags 29 May 2015, 21:05 Awesome! Thank you so much all! _________________ On the Kudos Spree. If you like my post/comment please appreciate with kudos Senior Manager Joined: 21 May 2015 Posts: 275 Concentration: Operations, Strategy GMAT 1: 750 Q50 V41 Followers: 5 Kudos [?]: 100 [0], given: 57 Re: An empty pool being filled with water at a constant rate [#permalink] ### Show Tags 01 Jun 2015, 01:53 B if the rates are constant the ratio of capacity is proportional to that of time x/8=2/3 ------- x = 5 hr 20 min _________________ Apoorv I realize that i cannot change the world....But i can play a part Optimus Prep Instructor Joined: 06 Nov 2014 Posts: 1782 Followers: 51 Kudos [?]: 393 [1] , given: 21 Re: An empty pool being filled with water at a constant rate [#permalink] ### Show Tags 02 Jun 2015, 08:13 1 This post received KUDOS Expert's post An empty pool being filled with water at a constant rate takes 8 hours to fill to 3/5 of its capacity. How much more time will it take to finish filling the pool? (3/5) An empty pool being filled with water at a constant rate takes 8 hours to fill to 3/5 of its capacity. How much more time will it take to finish filling the pool? (3/5) of a pool/ 8 hours = 3/40 (the rate) (3 pools/40 hours) = (2/5* pool)/ x hours Cross multiply 3x = (2/5) 40 3x = (2/5) (8) (5) 3x = 16 x = 16/3 or 5 1/3 1/3 of an hour = 20 minutes * The pool is 3/5 full so 2/5 remains. (A) 5 hr 30 min (B) 5 hr 20 min (C) 4 hr 48 min (D) 3 hr 12 min (E) 2 hr 40 min _________________ # Janielle Williams Customer Support Special Offer:$80-100/hr. Online Private Tutoring
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Re: An empty pool being filled with water at a constant rate [#permalink]

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17 May 2016, 04:59
We know,
R * T = Q , suppose the Q=100ltr. then,
R * 8 = 3/5 of 100 ==> 60/8 ==> 15/2 ltr per hour.

now, remaning 40ltr(which is 100 - 60 or 2/5 of 100)
R * t = Q
or, 15/2 * t = 40
or, t = 40 * 2/15
t = 16/3 = 5.33 = 5 hour + 1/3 and 1/3 of 60 = 20. so, 5 hour 20 mins.

If only such questions were asked in GMAT.
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Re: An empty pool being filled with water at a constant rate [#permalink]

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17 May 2016, 16:01
Walkabout wrote:
An empty pool being filled with water at a constant rate takes 8 hours to fill to 3/5 of its capacity. How much more time will it take to finish filling the pool?

(A) 5 hr 30 min
(B) 5 hr 20 min
(C) 4 hr 48 min
(D) 3 hr 12 min
(E) 2 hr 40 min

Solution:

To solve we can setup a proportion. The proportion will read:

A time of 8 hours is to filling up 3/5 of the pool is the same as a time of x number of hours is to filling up (the remaining) 2/5 of the pool. Setting this up mathematically we have:

8/(3/5) = x/(2/5)

8/(3/5) = x/(2/5)

40/3= 5x/2

Cross multiplying, we get:

80 = 15x

16 = 3x

16/3 = x

5 1/3 hours = x

5 hours and 20 minutes = x

Answer: B
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Re: An empty pool being filled with water at a constant rate   [#permalink] 17 May 2016, 16:01
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