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## Topic review (newest first)

bobbym
2012-10-07 07:30:20

Hi anna_g;

That is good to hear. Thanks for the problem.

anna_gg
2012-10-07 00:27:15

Yes!

bobbym
2012-10-06 22:32:50

Hi;

Do you know if we got the right answer?

anna_gg
2012-10-06 22:29:41

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!!

bobbym
2012-10-06 07:39:17

Hi anna_gg;

anonimnystefy
2012-10-06 03:47:59

I got

anna_gg
2012-10-05 22:54:21

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?