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**anna_gg****Member**- Registered: 2012-01-10
- Posts: 113

3 friends, Alan, Brian and Chester, paint a house. If Alan had to paint it on his own, it would take him one hour more than the time it would take for all three to paint it together. If Brian had to paint it on his own, it would take him five hours more than the time it would take for all three to paint it together, and Chester 8 hours more.

How much time would it take for Alan and Brian to paint it together?

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,521

I got

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,250

Hi anna_gg;

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**anna_gg****Member**- Registered: 2012-01-10
- Posts: 113

Let A, B and C be the hours needed for each friend to paint the house on his own and D the number of hours needed if they paint all together.

Then

A = D+1

B = D+5

C = D+8

In one hour, Alan has painted 1/A of the house, Brian 1/B and Chester 1/C, so all together have painted 1/A+1/B+1/C.

Thus in D hours they have painted D*(1/A+1/B+1/C) and we have:

D*(1/A+1/B+1/C)=1 (the entire house).

By substituting A, B and C from the above equations, we finally get:

D^3 + 7D^2-20=0. We keep the only acceptable solution D=1,531129 (the other two are negative).

So we have: A=2,531129 B=6,531129

Now that A and B will paint the house:

Let X be the number of hours we are looking for.

Χ*(1/A+1/B)=1. By substituting the above values of A and B, we get X = 1,824173, which is what you got, guys!

Thanks!!

*Last edited by anna_gg (2012-10-06 00:30:20)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,250

Hi;

Do you know if we got the right answer?

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**anna_gg****Member**- Registered: 2012-01-10
- Posts: 113

Yes!

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,250

Hi anna_g;

That is good to hear. Thanks for the problem.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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