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**Monox D. I-Fly****Member**- Registered: 2015-12-02
- Posts: 951

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)?

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**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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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,170

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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**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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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,170

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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**thickhead****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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**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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**Monox D. I-Fly****Member**- Registered: 2015-12-02
- Posts: 951

Thanks everyone. Thickhead was right, that was what I meant. Indonesian words are mostly derived from India, anyway.

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