Numerical answer
A and B together can complete a job in 12 days, B and C together in 15 days, and C and A together in 20 days. In how many days can A alone complete the job?
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Answer: 30
Add the three pairwise 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.
A's rate = (A + B + C) − (B + C) = 1/10 − 1/15 = (3 − 2)/30 = 1/30.
A alone needs 30 days.
Tip: With three pairwise rates, add them and halve to get the combined rate; subtract a pair to isolate one worker.
So A + B + C = 1/10 of the job per day.
A's rate = (A + B + C) − (B + C) = 1/10 − 1/15 = (3 − 2)/30 = 1/30.
A alone needs 30 days.
Tip: With three pairwise rates, add them and halve to get the combined rate; subtract a pair to isolate one worker.
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