A and B together can complete a task in 10 days, while B and C together can complete the same task in 15 days. If A, B, and C work together, how long will it take to complete the task?A)  5 days B) 6 days C) 7.5 days D) 8 days

To solve this problem, we need to find the rates at which A, B, and C work.

1. A and B together can complete the task in 10 days. So, their combined rate is 1 task/10 days = 0.1 tasks/day.

2. B and C together can complete the task in 15 days. So, their combined rate is 1 task/15 days = 0.067 tasks/day.

3. If we add these two rates together, we get a rate of 0.1 tasks/day + 0.067 tasks/day = 0.167 tasks/day. However, this rate includes B's work twice (once from A and B's rate, and once from B and C's rate).

4. To find the rate of A, B, and C together, we need to subtract B's rate from the combined rate. We can find B's rate by subtracting the rate of B and C from the rate of A and B. So, B's rate is 0.1 tasks/day - 0.067 tasks/day = 0.033 tasks/day.

5. Subtracting B's rate from the combined rate gives us the rate of A, B, and C together: 0.167 tasks/day - 0.033 tasks/day = 0.134 tasks/day.

6. To find out how long it will take A, B, and C to complete the task together, we divide the total task (1) by their combined rate: 1 task / 0.134 tasks/day = 7.46 days.

So, the closest answer is C) 7.5 days.