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

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20 Dec 2012, 05:53

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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

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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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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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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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.

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

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26 Apr 2014, 19:12

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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)....

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

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17 May 2016, 05:59

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.

gmatclubot

Re: An empty pool being filled with water at a constant rate
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17 May 2016, 05:59

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