Numerical answer
A and B together can finish a job in 12 days, B and C together in 15 days, and A and C together in 20 days. All three start working together, but A leaves after 4 days. In how many days from the start is the job completed?
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Answer: 13
Adding the three pair-rates: 2(A + B + C) = 1/12 + 1/15 + 1/20 = (5 + 4 + 3)/60 = 1/5, so A + B + C = 1/10 of the job per day.
In 4 days all three do 4/10 of the job. Remaining = 6/10.
B + C do 1/15 per day, so they need (6/10) ÷ (1/15) = 9 days.
Total = 4 + 9 = 13 days.
In 4 days all three do 4/10 of the job. Remaining = 6/10.
B + C do 1/15 per day, so they need (6/10) ÷ (1/15) = 9 days.
Total = 4 + 9 = 13 days.
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