SOLUTION: A can do half as much work as B in the same time and B can do one third as much work as C. If they can finish the work in 12 days, find in how many days can each finish the work.

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A can do half as much work as B in the same time and B can do one third as much work as C. If they can finish the work in 12 days, find in how many days can each finish the work.       Log On


   

Question 635716: A can do half as much work as B in the same time and B can do one third as much work as C. If they can finish the work in 12 days, find in how many days can each finish the work.
Solution:
Let C does 1 work in x days, then
C = 1/x, B = 1/3x, A = 1/16x
Total work = 1
or, 12(1/x + 1/3x + 1/6x) = 1
Or, x = 1/18
So, C = 18 days, B = 54 days, C = 108 days. Am I right ? I am not sure.
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

Let C does 1 work in x days, then

 C = 1/x, B = 1/3x, A = 1/6x

 Total work = 1

 or, 12(1/x + 1/3x + 1/6x) = 1

prefer to think of it in this manner: work/day

 (1/x + 1/3x + 1/6x) = 1/12    |Multiplying thru by 12x so as all denominators = 1

 12 + 4 + 2 = x

 Or, x = 18

 So, C = 18 days, B = 54 days, C = 108 days   Yes. Good Work.