SOLUTION: A can do a piece of work in 9 days, B in 12 days and C in 18 days. A & B work for 3 days after which C replaces B. How long must A & C work together to finish the job?

Question 880397: A can do a piece of work in 9 days, B in 12 days and C in 18 days. A & B work for 3 days after which C replaces B. How long must A & C work together to finish the job?
Found 2 solutions by ewatrrr, ankor@dixie-net.com:
Answer by ewatrrr(24785) (Show Source): You can put this solution on YOUR website!

Re TY
is the amount of work left to do.
After 3days
3/9 + 3/12 = 1/3 + 1/4 = 7/12 of work done
x/9 + x/18 = |Multiplying thru by 72 so as all denominators = 1
8x + 4x = 30
12x = 30
x = 30/12 = 2 1/2 days for A & C to finish

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A can do a piece of work in 9 days, B in 12 days and C in 18 days.
A & B work for 3 days after which C replaces B.
How long must A & C work together to finish the job?
:
let t = days A & C must work together to finish the job
Let the completed job = 1
:
A shared work equation
+ + = 1
multiply equatin by 36, cancel the denominators, you then have:
4(t+3) + 3(3) + 2t = 36
4t + 12 + 9 + 2t = 36
6t + 21 = 36
6t = 36 - 21
6t = 15
t = 15/6
t = 2.5 days A & C working together
;
:

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