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An empty pool being filled with water at a constant rate tak

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Intern
Joined: 23 Dec 2014
Posts: 49
Re: An empty pool being filled with water at a constant rate tak [#permalink]

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11 Feb 2015, 12:34
GMATD11 wrote:
An empty pool being filled with water at a constant rate takes 8hours to fill to 3/5 of its capacity.how much more time will it take to finish filling the pool?

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

Does 3/5 hour in 8 Hour.

Rest of the job = 1-3/5
= 2/5

3/5 work in 8 hour
2/5 work in = 8x5x2 / 3x8 =16/3

so. 5 hour 20 minutes.
Intern
Joined: 09 Jun 2015
Posts: 9
Re: An empty pool being filled with water at a constant rate tak [#permalink]

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02 Mar 2016, 19:35
Here is another quick way to find the solution.

3/5 of the pool is filled in 8 hours. Therefore, in total it takes 8/(3/5) hours to fill the pool.

Hence, 8/(3/5) - 8 = Remaining hours required to fill the pool
8/(3/5) - 8
= 40/3 - 24/3
= 16/3
= 5 and 1/3 hours or 5 hours and 20 minutes

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Joined: 17 Mar 2014
Posts: 160
An empty pool being filled with water at a constant rate tak [#permalink]

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28 Jan 2017, 10:24
Bunuel wrote:
GMATD11 wrote:
An empty pool being filled with water at a constant rate takes 8hours to fill to 3/5 of its capacity. how much more time will it take to finish filling the pool?
a)5hr 30min
b)5hr 20min
c)4hr 48min
d)3 hr 12min
e) 2hr 40 min

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

To fill 3/5 of the pool took 8 hours --> to fill 2/5 of the pool 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.

it took 8 hours to fill 3/5 of pool. Can't we consider it would have taken 2 hours to fill 1/5th of pool as rate is constant. so it will take 4hours to fill remaining 2/5th of pool ?
Math Expert
Joined: 02 Sep 2009
Posts: 43896
Re: An empty pool being filled with water at a constant rate tak [#permalink]

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28 Jan 2017, 10:29
ammuseeru wrote:
Bunuel wrote:
GMATD11 wrote:
An empty pool being filled with water at a constant rate takes 8hours to fill to 3/5 of its capacity. how much more time will it take to finish filling the pool?
a)5hr 30min
b)5hr 20min
c)4hr 48min
d)3 hr 12min
e) 2hr 40 min

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

To fill 3/5 of the pool took 8 hours --> to fill 2/5 of the pool 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.

it took 8 hours to fill 3/5 of pool. Can't we consider it would have taken 2 hours to fill 1/5th of pool as rate is constant. so it will take 4hours to fill remaining 2/5th of pool ?

HOW did you get this?

8 hours to fill 3/5 of pool
So, to fill 1/5th of the pool it'll take 3 times less, so 8/3 hours. Therefore to fill 2/5th it'll take twice as much time, so 16/3 hours.
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Re: An empty pool being filled with water at a constant rate tak [#permalink]

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22 Oct 2017, 04:09
Lets assume tank capacity is 100 ml

So 8 hrs ----for 3/5*100 =60 ml
x hrs------40 ml

So ....8/60 = x/40

x= 5.30

where am i going wrong here?
Math Expert
Joined: 02 Sep 2009
Posts: 43896
Re: An empty pool being filled with water at a constant rate tak [#permalink]

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22 Oct 2017, 04:49
santro789 wrote:
Lets assume tank capacity is 100 ml

So 8 hrs ----for 3/5*100 =60 ml
x hrs------40 ml

So ....8/60 = x/40

x= 5.30

where am i going wrong here?

Check arithmetic:

8/60 = x/40

x = 16/3.
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Re: An empty pool being filled with water at a constant rate tak [#permalink]

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22 Oct 2017, 05:21
thanks Bunuel but 16/3 =5.33 which would be equal to 5.30 then how come the answer is 5.20
Math Expert
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Posts: 43896
Re: An empty pool being filled with water at a constant rate tak [#permalink]

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22 Oct 2017, 05:30
santro789 wrote:
thanks Bunuel but 16/3 =5.33 which would be equal to 5.30 then how come the answer is 5.20

1/3rd of an hour is 20 minutes.
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An empty pool being filled with water at a constant rate tak [#permalink]

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22 Oct 2017, 09:34
GMATD11 wrote:
An empty pool being filled with water at a constant rate takes 8hours to fill to 3/5 of its capacity.how much more time will it take to finish filling the pool?

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

45-second approach: Find rate of filling. Find work remaining. Find time needed to finish: Work divided by rate equals time (to fill volume that needs filling).

What is rate of filling?
$$\frac{Work}{time} = rate$$

RATE = $$\frac{(\frac{3}{5})}{8} = (\frac{3}{5}*\frac{1}{8})= \frac{3}{40}$$

How much work remaining?
$$1 - (\frac{3}{5}) = (\frac{5}{5} - \frac{3}{5})= \frac{2}{5}$$

How much time to finish remaining work? $$\frac{Work}{rate} = time$$

Work remaining = $$\frac{2}{5}$$
Rate = $$\frac{3}{40}$$

$$\frac{(\frac{2}{5})}{(\frac{3}{40})}$$ =

$$\frac{2}{5} * \frac{40}{3} = 5\frac{1}{3}hrs$$

Multiply any fraction of an hour by 60 to get minutes.* In cases where you already have the hours, and you need hours plus minutes, use only the fraction. (Do not include the 5 here.)

$$\frac{1}{3}hr * 60 =$$ 20 minutes

$$5\frac{1}{3}hrs$$ = 5 hours, 20 minutes

*Because:

$$\frac{1hr}{3} * \frac{60min}{1hr} =$$ 20 minutes, where hours cancel

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

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28 Dec 2017, 06:12
Bunuel, niks18, amanvermagmat

How valid is this approach?
x = full capacity

Amount of work = Rate * no of hours
(3/5)*x = R1 *8 (first phase)
(2/5) *x = R2 * y (remaining phase/ capacity to fill)

Setting proportionality:

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

I am skipping extra steps since led to same answer choice, ie y = 16/3
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Joined: 09 Mar 2016
Posts: 250
Re: An empty pool being filled with water at a constant rate tak [#permalink]

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28 Dec 2017, 09:53
GMATD11 wrote:
An empty pool being filled with water at a constant rate takes 8hours to fill to 3/5 of its capacity.how much more time will it take to finish filling the pool?

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

Whats wrong with my solution ?

8 = 3/5
x=2/5 cross multiply... but in the end I get 16/3 = 5,333
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Joined: 02 Sep 2009
Posts: 43896
Re: An empty pool being filled with water at a constant rate tak [#permalink]

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28 Dec 2017, 09:58
1
KUDOS
Expert's post
dave13 wrote:
GMATD11 wrote:
An empty pool being filled with water at a constant rate takes 8hours to fill to 3/5 of its capacity.how much more time will it take to finish filling the pool?

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

Whats wrong with my solution ?

8 = 3/5
x=2/5 cross multiply... but in the end I get 16/3 = 5,333

Not sure what you are doing there but the answer you are getting is correct: 16/3 hours = 5 hours 20 minutes. This is explained in the solutions which are presented in this topic. It seems that you don't read the thread at all...
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An empty pool being filled with water at a constant rate tak [#permalink]

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28 Dec 2017, 10:01
Bunuel, niks18, amanvermagmat

How valid is this approach?
x = full capacity

Amount of work = Rate * no of hours
(3/5)*x = R1 *8 (first phase)
(2/5) *x = R2 * y (remaining phase/ capacity to fill)

Setting proportionality:

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

I am skipping extra steps since led to same answer choice, ie y = 16/3

The approach is fine. Can you think of a simpler way? try it out
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Re: An empty pool being filled with water at a constant rate tak [#permalink]

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20 Feb 2018, 15:05
Hi All,

We're told that 8 hours fills 3/5 of the pool; the question asks how long it will take to fill the remaining 2/5 of the pool. Since the pool is filling at a constant rate, we can use a ratio to answer the question. The ratio can be written in a number of different ways; I used:

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

Simplifying, we get…

8/X = 3/2

Now, cross-multiply…

3X = 16

X = 5 1/3 hours

[Reveal] Spoiler:
B

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Re: An empty pool being filled with water at a constant rate tak   [#permalink] 20 Feb 2018, 15:05

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