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#1 2012-10-05 00:54:21

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

House painting

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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#2 2012-10-05 05:47:59

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,525

Re: House painting

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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#3 2012-10-05 09:39:17

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,705

Re: House painting

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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#4 2012-10-06 00:29:41

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

Re: House painting

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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#5 2012-10-06 00:32:50

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,705

Re: House painting

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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#6 2012-10-06 02:27:15

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

Re: House painting

Yes!

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#7 2012-10-06 08:30:20

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,705

Re: House painting

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.

Online

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