we can determine the individual rates of work for A and B and calculate how much work they completed together in 8 days. Then, we can subtract that work from the total work to find the remaining work that B completed on their own.
Let's denote the total work as W.
A's rate of work: 1 work / 18 days
B's rate of work: 1 work / 24 days
Together, their combined rate of work is (1/18 + 1/24) works per day.
In 8 days, the amount of work they completed together is:
Work completed together = (1/18 + 1/24) * 8 = 8/18 + 8/24 = 4/9 + 1/3 = 12/27 + 9/27 = 21/27 = 7/9
The remaining work can be calculated as:
Remaining work = Total work - Work completed together = 1 - 7/9 = 2/9
B's rate of work is 1 work per 24 days, so to complete 2/9 of the work, B will take:
Time taken by B = (2/9) / (1/24) = (2/9) * (24/1) = 16/3 = \(5\frac{1}{3}\) days
Therefore, B will take approximately 16/3 days to complete the remaining work on their own.
