Question 646678
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