SOLUTION: If 8 men, 6 women, and 12 boys do a job in 24 days of 9 hours, in how many days of 8 hrs will 12 men, 15 women, & 10 boys do 3 times as much work, supposing 2 women do as much as

Question 781750: If 8 men, 6 women, and 12 boys do a job in 24 days of 9 hours,
in how many days of 8 hrs will 12 men, 15 women, & 10 boys do 3 times as much work,
supposing 2 women do as much as 5 boys &
1 man as much as 2 women?
I have worked on it and I finally came up with 50.5 days but I am not sure that that is the correct answer. Would appreciate knowing the correct answer.
Thanks

Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
If = rate of working in ( jobs ) / ( hour ), then
(1)
(2)
(3)
---------------------------
This is 3 equations and 3 unknowns, so I can solve it
From (2) and (3),

and, from (2),

-------------------------
Now, by substitution into (1),
(1)
(1)
(1)
(1)
(1)
(1)
--------------------------
From (2)and (3),

-----------------------
From (2),

----------------------
Let = hours to do work

Number of 8 hr days is:

30.575 8 hour days
check answer:
(1)

--------------------------
(1)
(1)
(1)
(1)
(1)
(1)
and
(2)
(2)
(2)
and
(3)
(3)

OK
The method is good, I think, but I could easily
made a mistake or 2

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