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Pipe A runs 30 liters of water per minute into a pool that

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Pipe A runs 30 liters of water per minute into a pool that

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Economist GMAT

Pipe A runs 30 liters of water per minute into a pool that has a total volume of 3,600 liters. Pipe B fill a third of the pool in 6 hours. Working together how long will it take both pipes to fill the pool?

A. 2 hours and 36 minutes
B. 1.5 hours
C. 9 hours and 12 minutes
D. 15 hours
E. 1 hour and 48 minutes

OA E.

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AAPL wrote:
Economist GMAT

Pipe A runs 30 liters of water per minute into a pool that has a total volume of 3,600 liters. Pipe B fill a third of the pool in 6 hours. Working together how long will it take both pipes to fill the pool?

A. 2 hours and 36 minutes
B. 1.5 hours
C. 9 hours and 12 minutes
D. 15 hours
E. 1 hour and 48 minutes

OA E.
Let's determine the COMBINED RATE of the two pipes

Given: Pipe A's RATE = 30 liters per minute
This is equivalent to 1800 liters per HOUR

Pipe B fills a third of the pool in 6 hours
So, Pipe B fills the ENTIRE pool (3600 liters) in 18 hours
Rate = Output/time
= 3600/18
= 200 liters per hour

COMBINED RATE = 1800 + 200
= 2000 liters per hour


Working together how long will it take both pipes to fill the pool?
Time = output/rate
= 3600/2000
= 36/20 hours
= 9/5 hours
= 1 4/5 hours
= 1 hour and 48 minutes
= E

Cheers,
Brent

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Brent Hanneson – Creator of GMATPrepNow.com
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AAPL wrote:
Economist GMAT

Pipe A runs 30 liters of water per minute into a pool that has a total volume of 3,600 liters. Pipe B fill a third of the pool in 6 hours. Working together how long will it take both pipes to fill the pool?

A. 2 hours and 36 minutes
B. 1.5 hours
C. 9 hours and 12 minutes
D. 15 hours
E. 1 hour and 48 minutes
The combined rate of pipes A and B is:

30/(1/60) + (1/3 x 3600)/6 = 1800 + 1200/6 = 1800 + 200 = 2000 liters per hour.

Thus, it will take 3600/2000 = 36/20 = 9/5 = 1 4/5 hours = 1 hour and 48 minutes to fill the pool when the two pipes work together.

Alternate Solution:

Pipe A’s rate is 30 liters per minute, or 1800 liters per hour. Pipe B’s rate is 1,200 liters in 6 hours, or 200 liters per hour. Thus, their combined hourly rate is 1800 + 200 = 2000 liters.

Thus, it will take 3600/2000 = 36/20 = 9/5 = 1 4/5 hours = 1 hour and 48 minutes to fill the pool when the two pipes work together.

Answer: E

_________________
Scott Woodbury-Stewart Founder and CEO

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AAPL wrote:
Economist GMAT

Pipe A runs 30 liters of water per minute into a pool that has a total volume of 3,600 liters. Pipe B fill a third of the pool in 6 hours. Working together how long will it take both pipes to fill the pool?

A. 2 hours and 36 minutes
B. 1.5 hours
C. 9 hours and 12 minutes
D. 15 hours
E. 1 hour and 48 minutes
$$?\,\,\,:\,\,\,{\rm{time}}\,\,{\rm{together}}\,\,{\rm{for}}\,\,3600\,\,{\rm{liters}}$$

Let´s use UNITS CONTROL, one of the most powerful tools of our method!

$$\left. \matrix{
A\,\,:\,\,\,{{30\,\,{\rm{liters}}} \over {\,1\,\,{\rm{minute}}\,}}\,\,\,\, \Rightarrow \,\,\,\,{{90\,\,{\rm{liters}}} \over {\,3\,\,{\rm{minutes}}\,}} \hfill \cr
B\,\,:\,\,\,\,{{1200\,\,{\rm{liters}}} \over {\,6\,\,{\rm{hours}}\,}}\,\,\,\left( {{{1\,\,{\rm{hour}}} \over {\,60\,\,{\rm{minutes}}\,}}} \right)\,\, = \,\,{{10\,\,{\rm{liters}}} \over {\,3\,\,{\rm{minutes}}\,}}\,\,\, \hfill \cr} \right\}\,\,\,\,\,\, \Rightarrow \,\,\,\,?\,\,\, = \,\,\,3600\,\,{\rm{liters}}\,\,\,\,\left( {{{3\,\,{\rm{minutes}}} \over {\,90 + 10\,\,{\rm{liters}}\,}}} \right)\,\,\, = \,\,\,108\min \,\,\, = \,\,\left( {60 + 48} \right)\,\,\min $$


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

_________________
Fabio Skilnik :: https://GMATH.net (Math for the GMAT) or https://GMATH.com.br (Portuguese version)
Course release PROMO : finish our test drive till 30/Nov with (at least) 50 correct answers out of 92 (12-questions Mock included) to gain a 50% discount!

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