SOLUTION: A,B,C can finish a piece of work in 60 days. They work together for 10 days after which A leaves, B and C continue for 20 days more days, after which B leaves. then C working for o

Question 646678: A,B,C can finish a piece of work in 60 days. They work together for 10 days after which A leaves, B and C continue for 20 days more days, after which B leaves. then C working for one-third longer each day completes the remaining work in 96 more days. If C had been working working at its own original rate then he would have completed the work in 222 days. How long would B take?
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
Let a, b, c be the three work rates
Working together, they can complete the job in 60 days:
a + b + c = 1 job/60 d = 1/60
After 10 days, the job is (1/60)*10 = 1/6 complete
B and C working together for 20 days complete this much of the job: 20(b+c)
Then C working alone completes the job in 96 days working 4/3 as much per day.
So C completes this much of the job: 96c(4/3) = 128c
C working alone can complete the job in 222 days, so c = 1/222
Since after the first 10 days 5/6 of the job gets completed, we can write:
5/6 = 128c + 20(b+c)
5/6 = 128/222 + 20b + 20/222
Simplifying gives 5/6 = 4/6 + 20b
b = (1/6)/20 = 1/120
So B can complete the job in 120 days
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