Author 
Message 
SVP
Joined: 03 Feb 2003
Posts: 1604

A certain swimming pool of 10000 liters has three pipes; [#permalink]
Show Tags
06 Aug 2003, 10:25
1
This post was BOOKMARKED
This topic is locked. If you want to discuss this question please repost it in the respective forum.
A certain swimming pool of 10000 liters has three pipes; pipe A to fill and pipes B and C to pour out. A fills the pool at 1000 liters per hour; B pours out at 200 lph; C pours out at 100 lph. All the pipes start to work simultaneously. Unfortunately, due to some problem, A stops for 5 minutes after each hour of working. B and C stop for 5 minutes after each half an hour of working. However, all the pipes work until the pool is full. How long does it take them to fill the pool completely?



Manager
Joined: 24 Jun 2003
Posts: 91
Location: Moscow

Re: SWIMMING POOL [#permalink]
Show Tags
06 Aug 2003, 10:56
stolyar wrote: A certain swimming pool of 10000 liters has three pipes; pipe A to fill and pipes B and C to pour out. A fills the pool at 1000 liters per hour; B pours out at 200 lph; C pours out at 100 lph. All the pipes start to work simultaneously. Unfortunately, due to some problem, A stops for 5 minutes after each hour of working. B and C stop for 5 minutes after each half an hour of working. However, all the pipes work until the pool is full. How long does it take them to fill the pool completely?
A admit I used a calculator because this challenge is not a 2,(027) min question.
Answers are:
7h54min with faulty A,B,C, vaults and
7h42min if A,B,C work constantly.
_________________
Respect,
KL



Manager
Joined: 24 Jun 2003
Posts: 91
Location: Moscow

The faulty valts answer is calculated on the conditions of a 5 min per hour break for all the vaults, where as the original Q states that B&C rest after every 30 min. Therefore, it will take some 1015 min faster to fill the pool.
My fault.
_________________
Respect,
KL



Manager
Joined: 22 Jul 2003
Posts: 62
Location: CA

Stolyar,
my answer comes to 15.01 hours



Manager
Joined: 24 Jun 2003
Posts: 91
Location: Moscow

Sorry guys, it's late in the evening here and I needed to eat some water melon to reconsider my answer. The exam date is approaching and I often catch myself thinking about it even in the most peculiar places.
Unswer is 15 hours.
Logic is as follows:
A pours in 1000*55/60 liters an hour (l/h)
B pours out 200*50/60 l/h
C pours out 100*50/60 l/h
To get a total amount of water that is added into the swimming pool every hour, substract B&C from A. It's 666,(6)liters.
Time=work/rate => 10000/666(6)=15 hours.
_________________
Respect,
KL



Manager
Joined: 22 Jul 2003
Posts: 62
Location: CA

We see that pipe A fills in 1000 gal in 65 minutes (1 hr filling and 5 min. rest).
We see that B & C drains out 300 gal. in 70 minutes (1/2 hr draining, 5 min rest, 1/2 hr draining and another 5 min. rest)
So, I suppose the total time taken is 910x. Why? Because, the LCM of 65 and 70 is 910. I used a factor x with it because I do not know yet whether 910 is the time taken in minutes, YET.
Now, A fills in 1000/65*910x gallons in 910x minutes
or, A fills in 14000x gallons
B&C drains 300/70*910x gallons in 910x minutes
or, B&C drains 3900x gallons
So, at the end of the total time (910x minutes) the pool will be filled.
=> 14000x  3900x = 10000
=> x = 10000/10100 = 100/101
So, total time = 910x
= 910 * 100/101
= 15.01 hours



GMAT Instructor
Joined: 07 Jul 2003
Posts: 770
Location: New York NY 10024
Schools: Haas, MFE; Anderson, MBA; USC, MSEE

Re: SWIMMING POOL [#permalink]
Show Tags
06 Aug 2003, 13:35
stolyar wrote: A certain swimming pool of 10000 liters has three pipes; pipe A to fill and pipes B and C to pour out. A fills the pool at 1000 liters per hour; B pours out at 200 lph; C pours out at 100 lph. All the pipes start to work simultaneously. Unfortunately, due to some problem, A stops for 5 minutes after each hour of working. B and C stop for 5 minutes after each half an hour of working. However, all the pipes work until the pool is full. How long does it take them to fill the pool completely?
Becareful the way you word/interpret the problems. The problem actually states that A stops working AFTER working for one hour, and pipes B and C stop working AFTER working for 30 minutes. This is entirely different than if A stops working once every hour (i.e., after working for 55 minutes) and B and C stop working once every half hour (i.e., after working 25 minutes), which is the problem that everyone solved.
Stolyar, what is your intention here?
_________________
Best,
AkamaiBrah Former Senior Instructor, Manhattan GMAT and VeritasPrep Vice President, Midtown NYC Investment Bank, Structured Finance IT MFE, Haas School of Business, UC Berkeley, Class of 2005 MBA, Anderson School of Management, UCLA, Class of 1993



Manager
Joined: 22 Jul 2003
Posts: 62
Location: CA

AkamaiBrah,
I don't agree. The problem states "A stops for 5 minutes after each hour of working. B and C stop for 5 minutes after each half an hour of working."
If "A stops working AFTER working for one hour, and pipes B and C stop working AFTER working for 30 minutes" then the pool will never be filled.



GMAT Instructor
Joined: 07 Jul 2003
Posts: 770
Location: New York NY 10024
Schools: Haas, MFE; Anderson, MBA; USC, MSEE

prakuda2000 wrote: AkamaiBrah, I don't agree. The problem states "A stops for 5 minutes after each hour of working. B and C stop for 5 minutes after each half an hour of working."
If "A stops working AFTER working for one hour, and pipes B and C stop working AFTER working for 30 minutes" then the pool will never be filled.
I'm sure he means 5 mnutes after each hour and half hour respectively, but your observation is besides my point. My point is that 5 minutes "after" each hour and halfhour is still different from 5 minutes "at the end" of each hour and halfhour respectively. The solution of 15 hours is the solution to the latter interpretation, which is not what Stolyar asked. The answer to the first interpretation is a few minutes less.
The answers are not different by much, BUT THEY ARE STILL DIFFERENT.
_________________
Best,
AkamaiBrah Former Senior Instructor, Manhattan GMAT and VeritasPrep Vice President, Midtown NYC Investment Bank, Structured Finance IT MFE, Haas School of Business, UC Berkeley, Class of 2005 MBA, Anderson School of Management, UCLA, Class of 1993



Manager
Joined: 10 Jun 2003
Posts: 210
Location: Maryland

great prblem [#permalink]
Show Tags
06 Aug 2003, 14:26
great problem...
the way i modeled this in order to be able to do this in about two minutes was to say that pipe A filled at a rate of 1000 * 11/12 lph and i mentally combined pipes B and C into one pipe emptying at 300 * 5/6 lph.
Then I set up the equation:
X (11000/12  1500/6) = 10000
By hand, X is about 15, a little more. Hope that is accurate enough for the GMAT!!!



Manager
Joined: 22 Jul 2003
Posts: 62
Location: CA

AkamaiBrah,
Absolutely. You are correct. I see what you mean. Currently trying to formulate a way to see if I can solve that. Thanks



SVP
Joined: 03 Feb 2003
Posts: 1604

Re: SWIMMING POOL [#permalink]
Show Tags
06 Aug 2003, 22:49
AkamaiBrah wrote: stolyar wrote: A certain swimming pool of 10000 liters has three pipes; pipe A to fill and pipes B and C to pour out. A fills the pool at 1000 liters per hour; B pours out at 200 lph; C pours out at 100 lph. All the pipes start to work simultaneously. Unfortunately, due to some problem, A stops for 5 minutes after each hour of working. B and C stop for 5 minutes after each half an hour of working. However, all the pipes work until the pool is full. How long does it take them to fill the pool completely? Becareful the way you word/interpret the problems. The problem actually states that A stops working AFTER working for one hour, and pipes B and C stop working AFTER working for 30 minutes. This is entirely different than if A stops working once every hour (i.e., after working for 55 minutes) and B and C stop working once every half hour (i.e., after working 25 minutes), which is the problem that everyone solved. Stolyar, what is your intention here?
Sure you are correct! A works for a COMPLETE HOUR (60 minutes) then stops for 5 minutes. B and C work for HALF AN HOUR (30 min) and then stop for 5 min. And so on and so forth, until the pull is full. I invented the question occasionally yesterday, so figures can be raw. A hint: reconsider rates. My solution is to go public soon.



SVP
Joined: 03 Feb 2003
Posts: 1604

My solution:
1. Unite pouring pipes in one that works at the rate of 300 lph
2. Translate nominal rates into actual ones.
Since we deal with minutes, it is reasonable to get rid of hours
the nominal R(fill)=1000/60 lpm
the nominal R(pour)=300/60 lpm
the actual R(fill)=1000/65=200/13 lpm (because of a 5minute stop after each 60 m)
the actual R(pour)=150/35=30/7 lpm (because of a 5minute stop after each 30 m)
WORK=RATE*TIME
10000=(200/1330/7)*X in minutes
X=910000/1010=901 munutes approximately, or 15 hours and 1 minute.










