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## #1 2017-03-10 18:35:04

Monox D. I-Fly
Member
From: Indonesia
Registered: 2015-12-02
Posts: 1,239

A water tub has 3 water channels. Channel I and II for filling the tub and channel III to empty it. Those 3 channels together fulfill the tub for 1 hour and 20 minutes. Channel I and II together fulfill the tub for 1 hour and 12 minutes from the empty condition. Channel II and III together fulfill the tub for 4 hours from the empty condition. The duration of each channel I and channel II fulfill the tub and channel III empties the tub are...

Well, I don't know where to start. But if channel I and II together (without channel III being open) fulfill the tub in 1 hour and 12 minutes, does it mean that channel III can empty the tub just within 8 minutes (because 01.20 - 01.12)?

Actually I never watch Star Wars and not interested in it anyway, but I choose a Yoda card as my avatar in honor of our great friend bobbym who has passed away. May his adventurous soul rest in peace at heaven.

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## #2 2017-03-10 18:55:41

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Hi;

What does fulfill mean here?

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #3 2017-03-10 20:26:44

bob bundy
Registered: 2010-06-20
Posts: 8,371

bobbym:  I think he means 'fill'.

Monox D. I-Fly:  I would do this as follows:

Let channel I fill at a rate of A units per minute; channel II at B units per minute; and channel III empty at C units per minute.  Let the tub contain V uniits.

Then we have

(A+B-C) x 80 = V and two more similar equations for you to work out.  Use these to find A, B and C in terms of V.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #4 2017-03-10 20:58:35

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Okay, thanks Bob.

Hi Monox D. I-Fly;

Bob's formulation of the problem will pop up if you just would set the problem up as a specific example. The set of equations is underdetermined, meaning it has fewer equations than unknowns. You will not get a unique answer but rather a set of possible solutions.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #5 2017-03-10 21:03:45

bob bundy
Registered: 2010-06-20
Posts: 8,371

hi bobbym,

I think it is ok.  There are four unknowns, A, B, C, and V but you can get A in terms of V and so on.

The duration of each channel I and channel II fulfill the tub ....

ie.  How long will it take to fill the tub using A on its own.  So the time will drop out without any 'V' in the answer.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #6 2017-03-10 23:41:18

Member
Registered: 2016-04-16
Posts: 1,086

fulfill the tub= fill the tub full ; However that is Indian English.

Last edited by thickhead (2017-03-10 23:42:09)

{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

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## #7 2017-03-11 06:36:59

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Hmmm, I thought Monox D. I-Fly hailed from Indonesia...

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #8 2017-03-12 15:56:02

Monox D. I-Fly
Member
From: Indonesia
Registered: 2015-12-02
Posts: 1,239