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cistern and pipe

by hemant_rajput » Mon Jan 28, 2013 8:54 am
Q28 . A tank of 425 liters capacity has been filled with water through two pipes, the first pipe having been opened 5 hours longer than the second. If the first pipe were open as long as the second pipe, the first pipe deliver half the amount of water delivered by second pipe; if the two pipes were open simultaneously, the tank would be filled up in 17 hours. How long was the second pipe open?
a. 10
b. 12
c. 15
d. 18
Last edited by hemant_rajput on Mon Jan 28, 2013 9:25 pm, edited 1 time in total.
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by tisrar02 » Mon Jan 28, 2013 12:35 pm
IMO:C

OA and Source??

I think your also missing an answer choice (E)
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by guerrero » Mon Jan 28, 2013 1:19 pm
I got an approximate ans as 15 .. It involves a very tedious calculation . Doesn't look like a typical GMAT Q .

Anyway , let me know the OA and I will post the solution .

thanks !
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by GMATGuruNY » Mon Jan 28, 2013 3:45 pm
Some crucial information seems to be missing.
I believe that the following reflects the problem's intent:
Yesterday, Al and Bill produced a lot of 425 widgets. Al worked for x+5 hours and Bill worked for x hours. In x hours, Al can produce half as many widgets as Bill can produce in x+5 hours. Working together, Al and Bill can produce the entire lot in 17 hours. What is the value of x?

a)10 hrs
b)12 hrs
c)15 hrs
d)18 hrs
Since Al and Bill can produce the entire lot in 17 hours, the combined rate for Al and Bill = w/t = 425/17 = 25 widgets per hour.

We can plug in the answers, which represent the value of x.
Given that the lot = 425, the combined rate = 25, and the difference between x and x+5 is 5, the correct answer is almost certainly a multiple of 5.

Answer choice C: Bill worked for x=15 hours, implying that Al worked for x+5 = 15+5 = 20 hours
In 15 hours, the number of widgets produced by Al and Bill working together = r*t = 25*15 = 375.
Remaining work = 425-375 = 50 widgets.

These 50 widgets must have been produced by Al during the 5 hours that he worked alone.
Thus, Al's rate = w/t = 50/5 = 10 widgets per hour.
Thus, Bill's rate = (combined rate for Al and Bill) - (Al's rate alone) = 25-10 = 15 widgets per hour.

In x=15 hours, the number of widgets produced by Al = r*t = 10*15 = 150 widgets.
In x+5=20 hours, the number of widgets produced by Bill = r*t = 15*20 = 300 widgets.
Success!
In x hours, Al produces half the number of widgets that Bill produces in x+5 hours.

The correct answer is C.
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by hemant_rajput » Mon Jan 28, 2013 9:24 pm
GMATGuruNY wrote:Some crucial information seems to be missing.
I believe that the following reflects the problem's intent:
Yesterday, Al and Bill produced a lot of 425 widgets. Al worked for x+5 hours and Bill worked for x hours. In x hours, Al can produce half as many widgets as Bill can produce in x+5 hours. Working together, Al and Bill can produce the entire lot in 17 hours. What is the value of x?

a)10 hrs
b)12 hrs
c)15 hrs
d)18 hrs
Since Al and Bill can produce the entire lot in 17 hours, the combined rate for Al and Bill = w/t = 425/17 = 25 widgets per hour.

We can plug in the answers, which represent the value of x.
Given that the lot = 425, the combined rate = 25, and the difference between x and x+5 is 5, the correct answer is almost certainly a multiple of 5.

Answer choice C: Bill worked for x=15 hours, implying that Al worked for x+5 = 15+5 = 20 hours
In 15 hours, the number of widgets produced by Al and Bill working together = r*t = 25*15 = 375.
Remaining work = 425-375 = 50 widgets.

These 50 widgets must have been produced by Al during the 5 hours that he worked alone.
Thus, Al's rate = w/t = 50/5 = 10 widgets per hour.
Thus, Bill's rate = (combined rate for Al and Bill) - (Al's rate alone) = 25-10 = 15 widgets per hour.

In x=15 hours, the number of widgets produced by Al = r*t = 10*15 = 150 widgets.
In x+5=20 hours, the number of widgets produced by Bill = r*t = 15*20 = 300 widgets.
Success!
In x hours, Al produces half the number of widgets that Bill produces in x+5 hours.

The correct answer is C.

Sorry guys, I missed the part during typing.

Anyways Guru has provided the complete question. Also I've modified the original post for anyone's future reference.
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by hemant_rajput » Tue Jan 29, 2013 8:06 am
guerrero wrote:I got an approximate ans as 15 .. It involves a very tedious calculation . Doesn't look like a typical GMAT Q .

Anyway , let me know the OA and I will post the solution .

thanks !
please stop giving such lame excuses. Just because you method takes time it doesn't mean other method don't exist.
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