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Pool Filling

by sam0575 » Sat May 10, 2014 1:11 am

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Hi,

Here's a problem I find quite hard to solve :

"An empty pool being filled with water at a constant rate take 8 hours to fill to 3/5 of its capacity. How much more time will it take to finish filling the pool ?"

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

Here's how I tried to fix the problem :

We know that 3/5 = 8xR
So R = 3/40
And 2/5 = Tx3/40, T being the remaining time to finish filling the pool.
So T = (2/5)/(3/40) = 5,33

Given this I would pick answer A. Still, the right answer is answer B...

I don't understand what's wrong in my reasoning ?

Thank you very much for your help :)
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by [email protected] » Sat May 10, 2014 1:27 am
Hi sam0575,

Since the pool is filling at a constant rate, we can use a ratio to answer the question.

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.

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

Final Answer: B

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by Brent@GMATPrepNow » Sat May 10, 2014 2:03 am
sam0575 wrote:An empty pool being filled with water at a constant rate take 8 hours to fill to 3/5 of its capacity. How much more time will it take to finish filling the pool ?

A. 5hr 30 min
B. 5hr 20 min
C. 4hr 48 min
D. 3hr 12 min
E. 2hr 40 min
We know it takes 8 hours to fill to 3/5 of its capacity.
We want to know how long it will take to fill the remaining 2/5 of capacity.

IMPORTANT: 2/5 is 2/3 as big as 3/5
So, if it takes 8 hours to fill 3/5 of the pool, then the time to fill 2/5 of the pool = (2/3)(8) hours = 16/3 hours = 5 1/3 hours = [spoiler]5 hours and 20 minutes = B[/spoiler]

Cheers,
Brent
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by GMATGuruNY » Sat May 10, 2014 2:18 am
sam0575 wrote:Hi,

Here's a problem I find quite hard to solve :

"An empty pool being filled with water at a constant rate take 8 hours to fill to 3/5 of its capacity. How much more time will it take to finish filling the pool ?"

A. 5hr 30 min
B. 5hr 20 min
C. 4hr 48 min
D. 3hr 12 min
E. 2hr 40 min
Let the capacity of the pool be the LCM of 5 and 8 = 40 liters.

3/5 of the pool's capacity = (3/5)(40) = 24 liters.
Since it takes 8 hours to pump these 24 liters into the pool, the pump's rate = w/t = 24/8 = 3 liters per hour.

Remaining liters to be pumped into the pool = 40-24 = 16 liters.
At a rate of 3 liters per hour, the time required to pump in the remaining 16 liters = 16/3 hours = 5 hours 20 minutes.

The correct answer is B.
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by Brent@GMATPrepNow » Sat May 10, 2014 2:24 am
sam0575 wrote:
"An empty pool being filled with water at a constant rate take 8 hours to fill to 3/5 of its capacity. How much more time will it take to finish filling the pool ?"

A. 5hr 30 min
B. 5hr 20 min
C. 4hr 48 min
D. 3hr 12 min
E. 2hr 40 min
Here's a slightly different approach.

It takes 8 hours to fill to 3/5 of its capacity.
So, in 1/3 the time, we'll fill 1/3 as much. In other words, in 8/3 hours we can fill 1/5 of the pool.

We want to know how long it will take to fill 2/5 of the pool.
So, it will take twice as long as 8/3 hours.
This means that, the time to fill 2/5 of the pool = 2(8/3) = 16/3 hours = 5 1/3 hours = [spoiler]5 hours and 20 minutes = B[/spoiler]

Cheers,
Brent

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by [email protected] » Sat May 10, 2014 11:19 am
Hi sam0575,

In answer to your original question, your approach was fine, but since you did not label your units, you weren't clear on what your last line of math "meant."

You wrote 5,33, which means 5 1/3.

5 1/3 hours = 5hr 20 min

This can best be described as a silly mistake, but it's these same types of silly mistakes that tend to kill Test Takers. As you continue to practice, be sure to label your work and you'll minimize these mistakes.

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by sam0575 » Sun May 11, 2014 11:08 pm
Thank you very much for your answers !

Thanks Rich for explaining my silly mistake and for your advices !

Samuel.
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by Jeff@TargetTestPrep » Wed Jul 08, 2015 9:10 am
sam0575 wrote:Hi,

Here's a problem I find quite hard to solve :

"An empty pool being filled with water at a constant rate take 8 hours to fill to 3/5 of its capacity. How much more time will it take to finish filling the pool ?"

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

Here's how I tried to fix the problem :

We know that 3/5 = 8xR
So R = 3/40
And 2/5 = Tx3/40, T being the remaining time to finish filling the pool.
So T = (2/5)/(3/40) = 5,33

Given this I would pick answer A. Still, the right answer is answer B...

I don't understand what's wrong in my reasoning ?

Thank you very much for your help :)
Solution:

We can let x to be the number of hours needed to fill the remaining 2/5 of the pool. To solve we can set up 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(2/5) = x(3/5)

16/5 = 3x/5

Multiplying both sides by 5, we get:

16 = 3x

16/3 = x

5 1/3 hours = x

5 hours and 20 minutes = x

Answer: B

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