Final answer:
Calculating working rates, it has been determined that 'b' alone can complete the work in 24 days. This is solved by setting and solving an equation based on the combined and individual rates of work for 'a' and 'b'. The correct answer is c. 24 days.
Step-by-step explanation:
To find out how long it would take for b alone to do the work, we need to think about the work in terms of rates. The rate at which work is done is often expressed in units of work per day. Let's define the rates of work for a and b, as well as their combined rate when working together.
According to the problem, a and b together can complete the work in 8 days. This means their combined work rate is 1 work unit / 8 days. It is also given that a alone can complete the work in 12 days, which means a's work rate is 1 work unit / 12 days. We are asked to find the time it takes for b alone to complete the work, which we will call 'x' days, indicating b's work rate is 1 work unit / x days.
Since the rates of work add up when a and b work together, we can create the following equation to represent their combined work rate:
1/12 + 1/x = 1/8
To solve for 'x', we find a common denominator and solve for b's work rate.
1/x = 1/8 - 1/12
1/x = 3/24 - 2/24
1/x = 1/24
Therefore, we can see that b alone can complete the work in 24 days, so the correct answer is c. 24 days.