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        riddles >> medium >> House painting
        
(Message started by: Altamira_64 on Oct 5^th, 2012, 1:58am)

Title: House painting
Post by Altamira_64 on Oct 5^th, 2012, 1:58am

3 friends, Albert, Bob and Charly, paint a house. If Albert 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 Bob 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 Charly 8 hours more.
How much time would it take for Albert and Bob to paint it together?

Title: Re: House painting
Post by Altamira_64 on Oct 15^th, 2012, 1:18pm

Suppose A is the number of hours that Albert would need to paint it on his own, B for Bob, C for Charly and D the number of hours if the 3 of them painted the house together.
Then
A = D + 1
B = D + 5
C = D + 8
In one hour, A will have painted 1/A of the house, B 1/B and C 1/C, so all together:
1/A + 1/B + 1/C, so in D hours they have painted the entire house:

D*(1/A + 1/B + 1/C) = 1 (the entire house),
thus, replacing A B and C from the above equations, we get:
D^3 + 7D^2 – 20 = 0
By solving, we keep the only acceptable solution (sqrt(65)-5)/2 = 1,531129 (the other two solutions are negative).
So A = 2,531129 and B = 6,531129
So now suppose X is the number of hours we are looking for. We have:

Χ*(1/A+1/B)=1 and by solving we get X = 1,824173

Title: Re: House painting
Post by marlonmark on Jan 6^th, 2013, 10:34pm

That seems funny by answering your own question