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Math Expert V
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An empty pool being filled with water at a constant rate takes 8 hours  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 77% (01:38) correct 23% (01:49) wrong based on 1115 sessions

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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

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An empty pool being filled with water at a constant rate takes 8 hours  [#permalink]

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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

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 $$\frac{8}{(\frac{3}{5})}*\frac{2}{5} = \frac{16}{3} \ hours = 5 \ hours \ 20 \ minutes$$ (because if t is the time needed to fill the pool then $$t*\frac{3}{5}=8$$ --> $$t=8*\frac{5}{3} \ hours$$ --> to fill 2/5 of the pool $$8*\frac{5}{3}*\frac{2}{5}=\frac{16}{3}$$ 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: $$time = \frac{job}{rate} = \frac{2}{(\frac{3}{8})} = \frac{16}{3} \ hours = 5 \ hours \ 20 \ minutes$$.

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Re: An empty pool being filled with water at a constant rate takes 8 hours  [#permalink]

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Its B
I would use percentages to do this ... easy for me

3/5 work = 60% = is done in 8 hrs
remaining will be 40%( percentages are always 100) be done in 8*40/60 = 16/3 = 5 1/3 hrs = 5+1/3*60 = 5.20 hrs

PS:Edited for a typo

Originally posted by sudhir18n on 11 Jun 2011, 00:05.
Last edited by sudhir18n on 11 Jun 2011, 00:08, edited 2 times in total.
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Re: An empty pool being filled with water at a constant rate takes 8 hours  [#permalink]

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1st convert to mins to avoid the confusion

60% = 480 mins
therefore 40% (remaining) = 320 mins (using unitary method)

320 mins = 5 hrs 20 mins
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Re: An empty pool being filled with water at a constant rate takes 8 hours  [#permalink]

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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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Re: An empty pool being filled with water at a constant rate takes 8 hours  [#permalink]

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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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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: An empty pool being filled with water at a constant rate takes 8 hours  [#permalink]

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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

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Re: An empty pool being filled with water at a constant rate takes 8 hours  [#permalink]

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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.
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Re: An empty pool being filled with water at a constant rate takes 8 hours  [#permalink]

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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?

(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
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Re: An empty pool being filled with water at a constant rate takes 8 hours  [#permalink]

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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

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

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Re: An empty pool being filled with water at a constant rate takes 8 hours  [#permalink]

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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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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: An empty pool being filled with water at a constant rate takes 8 hours  [#permalink]

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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

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Re: An empty pool being filled with water at a constant rate takes 8 hours  [#permalink]

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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

Here's another approach:

IMPORTANT CONCEPT: After 8 hours, 3/5 of the job is finished and 2/5 of the job is remaining.
This means the remaining part of the job is 2/3 the size of the first part of the job.

Think of it this way:
If the pool had a capacity of 5 gallons, then the first part of the job would be filling 3 gallons, and the remaining part of the job is filling 2 gallons.
So, the remaining part of the job (filling 2 gallons) is 2/3 the size of the first part of the job (filling 3 gallons)

So, if it takes 8 hours to do the first part of the job, then the time to do the remaining part = 2/3 of 8 hours
2/3 of 8 hours = 2/3 x 8 hours
= 16/3 hours
= 5 1/3 hours
= 5 hours 20 minutes

Cheers,
Brent
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Re: An empty pool being filled with water at a constant rate takes 8 hours  [#permalink]

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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

We can let n = the time it takes to fill the remaining 2/5 of the pool and create the proportion:

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

40/3 = 5n/2

80 = 15n

n = 80/15 = 16/3 = 5 1/3 hours = 5 hours and 20 minutes

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Re: An empty pool being filled with water at a constant rate takes 8 hours  [#permalink]

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3/5 full in 8 hours (rest = 1-(3/5) = 2/5)
2/5 is filled in (8*5*20)/3*5 = 8 hour 20 minutes
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Re: An empty pool being filled with water at a constant rate takes 8 hours  [#permalink]

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Bunuel 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

Let the capacity of the pool be $$40$$ Units ( LCM of 5 & 8)

So, in 8 Hours the pipe fills $$24$$ units; Thus efficiency of the pipe is 3units/Hour

Time required to fill the entire pool is $$\frac{16}{3}$$ hours = $$5\frac{1}{3} = 5 Hours 20 Min$$; Answer must be (B)
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Re: An empty pool being filled with water at a constant rate takes 8 hours  [#permalink]

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3/5 of the capacity takes =8 hours
So whole capacity will take =8*(5/3)=40/3 hours
More times needed=(40/3)-8=16/3= 5 hours 20 minutes.

Posted from my mobile device Re: An empty pool being filled with water at a constant rate takes 8 hours   [#permalink] 06 May 2019, 20:28
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