Convert each worker’s time into a rate of work per day (1 ÷ days needed), add the rates together for combined work, then take the reciprocal to find the combined time.
The key idea: if someone can finish a job in "n" days working alone, they complete 1/n of the job per day. Once everyone's rate is in this "work per day" form, rates can simply be added together.
Question: A can finish a task in 10 days. B can finish the same task in 15 days. How long will it take if they work together?
Solution: A's rate = 1/10 per day. B's rate = 1/15 per day. Combined rate = 1/10 + 1/15 = 3/30 + 2/30 = 5/30 = 1/6 per day. Working together, they finish the task in 6 days.
If A and B work together for 2 days, then A leaves, and B finishes alone: after 2 days, 2 × (1/6) = 1/3 of the work is done, leaving 2/3 remaining. At B's rate of 1/15 per day, the remaining time is (2/3) ÷ (1/15) = 10 days.
This "rate per unit time" approach is the same underlying logic used in related questions about pipes filling or draining a tank.
Last reviewed: September 2026