Video narration
Several workers, different days, changing efficiency—and each question seems to need a new trick. Picture a team digging one pile. A worker finishing in T days completes 1/T of it each day: one-day work. Stop treating T as the answer. Convert each worker into one-day work first. Work = Rate × Time. Set the whole pile to one job, so rate is one divided by time. Together, add daily rates, not times: A + B = 1/A-time + 1/B-time. Take the reciprocal for combined time. More equal-efficiency workers mean less time; double efficiency, half the time. Example: A takes 6 days, B takes 3. Their rate is 1/6 plus 1/3, or 1/2 job per day, so they finish in 2 days. For partial work, subtract completed work from one, then divide the remainder by the new rate. Picture the team: shares first, time second.