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**Deon588****Member**- Registered: 2011-05-02
- Posts: 68

Hi all. Am I doing this correctly?

Question

In a factory 2 different machines A and B are used to fill bottles When the machines work together they fill the bottles in 2 hours. Machine A works twice as fast as machine B, how long does it take machine B to fill the bottles when it works alone? What i've done:

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**Deon588****Member**- Registered: 2011-05-02
- Posts: 68

I see some of the LaTeX lines are very close to each other. Is there a way to avoid this? Or should I just leave a line open?

Thanks in advance

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

I took care of the latex.

Did you check the answer you got?

**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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**Deon588****Member**- Registered: 2011-05-02
- Posts: 68

Thanks a lot Bobbym. so

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,203

hi Deon588,

That looks good to me.

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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**Deon588****Member**- Registered: 2011-05-02
- Posts: 68

So it will take Machine B 4 hours to fill the bottles?

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,203

hi deon588

You've used x for how long B will take on its own and worked out x = 360 minutes.

That isn't 4 hours!

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

Hi deon588;

How did you get 4 hours?

**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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**Deon588****Member**- Registered: 2011-05-02
- Posts: 68

Hi Bob. That's the part which confuses me. isn't

Thanks a lot for checking

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,203

My answer:

**Let x represent the time in minutes for machine B to fill N bottles.**

measured in bottles/minute

and as A does the same number of bottles twice as fast

So working together

Cancelling the Ns and simplfying the LHS

Invert both fractions

So machine B takes 360 minutes or 6 hours.

Check. With no loss of generality I can suppose that N = 720.

Then B's rate per minute is 720/360 = 2 bottles per minute.

So A's rate must be 4 bottles per minute.

So together they can do 6 bottles per minute.

So they can do 720 in 720/6 minutes = 120 minutes = 2 hours. "tick"

Note: I was taught to start by introducing what x stands for. Look at my first line in bold text.

That makes it easier for someone to follow your working.

And at the end you know what you have worked out!!!

Bob

*Last edited by bob bundy (2011-10-11 00:31:27)*

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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**Deon588****Member**- Registered: 2011-05-02
- Posts: 68

Bob thanks a lot for that very detailed explanation, as usual u completely cleared it up for me:).

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,203

hi

That's good to know. It's a pleasure to be of help!

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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