SOLUTION: Working alone, two painters, A and B, can paint a building in 12 and 16 days respectively. After they work together for 3 days, A leaves and B continues for 2 more days. Then C joi

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Working alone, two painters, A and B, can paint a building in 12 and 16 days respectively. After they work together for 3 days, A leaves and B continues for 2 more days. Then C joi      Log On


   

Question 427897: Working alone, two painters, A and B, can paint a building in 12 and 16 days respectively. After they work together for 3 days, A leaves and B continues for 2 more days. Then C joins B and they finish the job in 3 more days. In what time could C do the whole job alone?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Working alone, two painters, A and B, can paint a building in 12 and 16 days respectively.
After they work together for 3 days, A leaves and B continues for 2 more days.
Then C joins B and they finish the job in 3 more days.
In what time could C do the whole job alone?
:
Let c = time required by c to do the job alone
:
Let the completed job = 1
:
From the information we know that
A works for 3 days
B works 3 + 2 + 3 = 8 days
C works 3 days
:
3%2F12 + 8%2F16 + 3%2Fc = 1
Reduce the fractions a common denominator of 4
1%2F4 + 2%2F4 + 3%2Fc = 1
Multiply by 4c to clear the denominators, results:
c + 2c + 4(3) = 4c
:
3c + 12 = 4c
:
12 = 4c - 3c
:
c = 12 days alone is C's time
:
:
Check this:
3%2F12 + 8%2F16 + 3%2F12 =
1%2F4 + 2%2F4 + 1%2F4 = 1; confirms our solution of 12 days