Final answer:
B can finish the remaining work in 9 days and 8 hours after A leaves. The solution involves calculating the combined work rate of A and B, determining how much work is left after 12 days, and then calculating how much more time B requires solo to complete the work. Therefore, B will finish the remaining work in 9 days and 8 hours.
Step-by-step explanation:
A can complete a piece of work in 48 days, which means A can do ⅓ or 1/48 of the work in one day. Similarly, B can finish the work in 60 days, which means B can do ⅓ or 1/60 of the work in one day. When they work together for 12 days, they can complete (1/48 + 1/60) * 12 days of work.
This simplifies to (5/240 + 4/240) * 12, which simplifies further to 9/240 * 12, and then to 9/20 of the work which is completed. Therefore, 11/20 of the work remains.
To find out how long it will take B to finish the remaining 11/20 of the work alone, we divide the remaining fraction by B's daily work rate: (11/20) / (1/60) = 11/20 * 60. The result is 33 days.
Since B has already worked for 12 days, he needs an additional 21 days. However, since the question asks for the time beyond the initial 12 days A and B worked together, B will only need to work 9 more days on his own.
Since B can do 1/60 of the work in a day, to find out how many hours it will take B to finish 1/20 of the work on the last day, we calculate (1/60) / (1/20) = 1/3. This means B needs 1/3 of a day to finish the work. There are 24 hours in a day, so B needs 8 hours on the last day.
Therefore, B will finish the remaining work in 9 days and 8 hours.