SOLUTION: Andrew, Beth, and Carlos are painting a house. If Andrew and Beth paint the house together, it will take 10 days. If Beth and Carlos paint the house together , it will take 6 days.

Question 731272: Andrew, Beth, and Carlos are painting a house. If Andrew and Beth paint the house together, it will take 10 days. If Beth and Carlos paint the house together , it will take 6 days. If Andrew, Beth and Carlos all paint together, it will take 5 days. How long will it take Carlos to paint the house alone?
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Add rates of painting to get rate of
painting together
Let = Andrew's time in days to paint house alone
Let = Beth's time in days to paint house alone
Let = Carlos's time in days to paint house alone
For example:
( 1 house ) / ( a days ) + ( 1 house ) / ( b days ) = ( 1 house ) / ( 10 days )
(1)
(2)
(3)
---------------------------
make these substitutions:

-------------
(1)
(2)
(3)
----------------------------
(1)
and
(2)
------------------------
By substitution:
(3)
(3)
(3)
(3)
(3)
and
(2)
(2)
(2)
(2)
(2)
It will take Carlos 10 days to paint the house alone
check:
(1)
(1)
(1)
(1)
------------------
(3)
(3)
(3)
(3)
(3)
OK

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