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M19-04

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M19-04  [#permalink]

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New post 16 Sep 2014, 01:05
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A
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C
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Difficulty:

  5% (low)

Question Stats:

91% (01:04) correct 9% (01:07) wrong based on 187 sessions

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Valve 1, if open, would fill a pool in 3 hours. Valve 2, if open, would fill the pool in 6 hours. If both valves are opened simultaneously, how long will it take to fill the pool to \(\frac{1}{5}\) of its capacity?

A. 18 minutes
B. 20 minutes
C. 24 minutes
D. 30 minutes
E. 36 minutes

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New post 16 Sep 2014, 01:05
1
Official Solution:

Valve 1, if open, would fill a pool in 3 hours. Valve 2, if open, would fill the pool in 6 hours. If both valves are opened simultaneously, how long will it take to fill the pool to \(\frac{1}{5}\) of its capacity?

A. 18 minutes
B. 20 minutes
C. 24 minutes
D. 30 minutes
E. 36 minutes

The valves could fill the whole pool in \(\frac{1}{\frac{1}{3} + \frac{1}{6}} = 2\) hours. Therefore they would fill a fifth of the pool in \(\frac{2}{5}*60 = 24\) minutes.

Answer: C
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Re: M19-04  [#permalink]

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New post 27 Jul 2017, 04:35
Hi, i got the correct answer but it took me around 4minutes. I did it in a different way though...
Can you explain why you divide 1/1/3+1/6?? I really don´t get it.
Thanks


Bunuel wrote:
Official Solution:

Valve 1, if open, would fill a pool in 3 hours. Valve 2, if open, would fill the pool in 6 hours. If both valves are opened simultaneously, how long will it take to fill the pool to \(\frac{1}{5}\) of its capacity?

A. 18 minutes
B. 20 minutes
C. 24 minutes
D. 30 minutes
E. 36 minutes

The valves could fill the whole pool in \(\frac{1}{\frac{1}{3} + \frac{1}{6}} = 2\) hours. Therefore they would fill a fifth of the pool in \(\frac{2}{5}*60 = 24\) minutes.

Answer: C
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Re: M19-04  [#permalink]

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New post 27 Jul 2017, 04:54
1
juanito1985 wrote:
Hi, i got the correct answer but it took me around 4minutes. I did it in a different way though...
Can you explain why you divide 1/1/3+1/6?? I really don´t get it.
Thanks


Bunuel wrote:
Official Solution:

Valve 1, if open, would fill a pool in 3 hours. Valve 2, if open, would fill the pool in 6 hours. If both valves are opened simultaneously, how long will it take to fill the pool to \(\frac{1}{5}\) of its capacity?

A. 18 minutes
B. 20 minutes
C. 24 minutes
D. 30 minutes
E. 36 minutes

The valves could fill the whole pool in \(\frac{1}{\frac{1}{3} + \frac{1}{6}} = 2\) hours. Therefore they would fill a fifth of the pool in \(\frac{2}{5}*60 = 24\) minutes.

Answer: C


(rate)(time) = (job done)

So, (time) = (job done)/(rate).

The combined rate of the valves is \(\frac{1}{3} + \frac{1}{6}\). Hence \(\frac{1}{\frac{1}{3} + \frac{1}{6}} = 2\)
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Re: M19-04  [#permalink]

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New post 27 Jul 2017, 05:01
Bunuel wrote:
juanito1985 wrote:
Hi, i got the correct answer but it took me around 4minutes. I did it in a different way though...
Can you explain why you divide 1/1/3+1/6?? I really don´t get it.
Thanks


Bunuel wrote:
Official Solution:

Valve 1, if open, would fill a pool in 3 hours. Valve 2, if open, would fill the pool in 6 hours. If both valves are opened simultaneously, how long will it take to fill the pool to \(\frac{1}{5}\) of its capacity?

A. 18 minutes
B. 20 minutes
C. 24 minutes
D. 30 minutes
E. 36 minutes

The valves could fill the whole pool in \(\frac{1}{\frac{1}{3} + \frac{1}{6}} = 2\) hours. Therefore they would fill a fifth of the pool in \(\frac{2}{5}*60 = 24\) minutes.

Answer: C


(rate)(time) = (job done)

So, (time) = (job done)/(rate).

The combined rate of the valves is \(\frac{1}{3} + \frac{1}{6}\). Hence \(\frac{1}{\frac{1}{3} + \frac{1}{6}} = 2\)


Got it! Very straight forward. Thank you so much!
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Re: M19-04  [#permalink]

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New post 27 Jul 2017, 06:16
+1 for C. Use time and rate approach to solve this question. Both can fill the tank in 2 hours. To fill 1/5 of the tank we need (2/5)*60 or 24 minutes.
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M19-04  [#permalink]

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New post 27 Jul 2017, 06:28
1
Bunuel wrote:
Valve 1, if open, would fill a pool in 3 hours. Valve 2, if open, would fill the pool in 6 hours. If both valves are opened simultaneously, how long will it take to fill the pool to \(\frac{1}{5}\) of its capacity?

A. 18 minutes
B. 20 minutes
C. 24 minutes
D. 30 minutes
E. 36 minutes


Valve \(1\) can fill pool in \(3\) hours.
Valve \(1\) per hour rate of work \(= \frac{1}{3}\)

Valve \(2\) can fill pool in \(6\) hours.
Valve \(2\) per hour rate of work \(= \frac{1}{6}\)

\(1\) hour rate of work of Valve \(1\) and Valve \(2\) working together is;

\(\frac{1}{3} + \frac{1}{6} = \frac{2 + 1}{6} = \frac{3}{6} = \frac{1}{2}\)

Both valves working together can fill the pool in \(= \frac{1}{(1/2)} = 2\) hours \(= 120\) minutes

Therefore both valves working together can fill the pool to \(\frac{1}{5}\) of its capacity in \(= \frac{1}{5} * 120 = 24\) minutes

Answer (C)...
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Re: M19-04  [#permalink]

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New post 28 Jul 2017, 00:45
A - 1/3 Per Hour

B = 1/6 Per Hour

A & B together 1/3 + 1/6 = 1/2 per hour

we want to calculate the time for 1/5 of the pool

= 60 * 1/5 = 1/2 * x

x = 60 * 1/5 * 2

x = 24 minutes

hence, C
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Re: M19-04   [#permalink] 28 Jul 2017, 00:45
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