SOLUTION: 12 children and 18 men complete a certain piece of artwork in 9 days. Each child takes twice the time taken by a man to finish the artwork. In how many days will 18 men take

Algebra ->  Test -> SOLUTION: 12 children and 18 men complete a certain piece of artwork in 9 days. Each child takes twice the time taken by a man to finish the artwork. In how many days will 18 men take       Log On


   

Question 1132323: 12 children and 18 men complete a certain piece of
artwork in 9 days. Each child takes twice the time taken by
a man to finish the artwork. In how many days will 18
men take to finish the same artwork?






Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
2r, one man's rate
r, one child's rate

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12 children and 18 men complete a certain piece of
artwork in 9 days.
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%2812r%2B18%2A2r%29%2A9=1
48r=1%2F9
r=1%2F%289%2A48%29
r=1%2F432


Time for just 18 men to do the one piece of work:
18%2A2%281%2F%28432%29%29%2At=1

t=432%2F36

highlight%28t=12%29days

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


There are dozens of ways to solve this kind of problem. Here is what I would do....

A child takes twice as much time as a man to do the artwork.
So each child is worth half of a man.
Then 12 children are worth 6 men.
The given information then says that 18+6=24 men would take 9 days to finish the artwork.
24 men times 9 days equals 216 man-days.
216 man-days divided by 18 men equals 12 days.

ANSWER: 12 days