Video narration
How many more days does B need to finish the household chore after A leaves? Think of the whole chore as one complete job. Each person's completion time tells you how much of that job they do in one day. So we use daily contributions, not the two numbers added together. If A alone takes 16 days, A completes 1/16 of the chore each day. B, taking 12 days alone, completes 1/12 each day. Working together, add those contributions: 1/16 plus 1/12 equals 3/48 plus 4/48, or 7/48 of the chore per day. They work together for four days, so they finish 4 times 7/48, which is 7/12 of the chore. That leaves 1 minus 7/12, or 5/12, unfinished when A leaves. B now continues alone. Divide the remaining 5/12 by B's daily rate, 1/12. The twelfths cancel, leaving 5. So after A leaves, B needs 5 days to finish the chore.