Numerical answer
A and B together can finish a job in 9 days, B and C together in 14 days, and C and A together in 18 days. All three start working together, but A leaves after 3 days. In how many more days will B and C finish the remaining work?
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Answer: 9
Add the three pair-rates: 2(A + B + C) = 1/9 + 1/14 + 1/18 = (14 + 9 + 7)/126 = 30/126 = 5/21, so A + B + C = 5/42 per day.
In 3 days all three complete 3 × 5/42 = 15/42 = 5/14 of the job; 9/14 remains.
B + C = 1/14 per day, so the remaining work takes (9/14) ÷ (1/14) = 9 days.
Tip: Adding all pairwise rates double counts each worker exactly once — a quick route to the combined rate.
In 3 days all three complete 3 × 5/42 = 15/42 = 5/14 of the job; 9/14 remains.
B + C = 1/14 per day, so the remaining work takes (9/14) ÷ (1/14) = 9 days.
Tip: Adding all pairwise rates double counts each worker exactly once — a quick route to the combined rate.
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