SOLUTION: 20 hens housed in 3 pens will hatch 30 eggs in 80 days. How long will it take 30 hens in 4 pens to hatch the same number of eggs? A roofer takess 12 hours to shingle a roof al

Question 345137: 20 hens housed in 3 pens will hatch 30 eggs in 80 days. How long will it take 30 hens in 4 pens to hatch the same number of eggs?

A roofer takess 12 hours to shingle a roof alone.The roofer and his apprentice work 3 hours,then the roofer quits. The apprentice takes another 12 hours to finish the roof. How long would it take the apprentice alone?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
20 hens housed in 3 pens will hatch 30 eggs in 80 days.
How long will it take 30 hens in 4 pens to hatch the same number of eggs?
:
What has the number of pens got to do with it? Ignore that.
:
Find the number of hen-days required to hatch 30 eggs
20*80 = 1600 hen days to hatch 30 eggs
:
Let d = no. of days required by 30 hens to do the same thing
30d = 1600
d =
d = 53 days for 30 hens to hatch 30 eggs
:
:
A roofer takes 12 hours to shingle a roof alone.
The roofer and his apprentice work 3 hours, then the roofer quits.
The apprentice takes another 12 hours to finish the roof.
How long would it take the apprentice alone?
:
Let a = time required by the apprentice alone
Let the completed job = 1
:
The apprentice works a total of 15 hrs, therefore the equation is:
+ = 1
multiply eq by 12a, results:
3a + 12(15) = 12a
180 = 12a - 3a
180 = 9a
a =
a = 20 hrs alone for the apprentice
:
:
Check solution
+ =
reduce fractions
+ = 1; confirms our solution of a = 20

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