Let's break down the solution step by step.

Step 1: Calculate the rate of work for A, B, and C.

• A can complete the work in 5 days. So, A’s rate of work = $\frac{1}{5}$ of the work per day.
• B can complete the work in 10 days. So, B’s rate of work = $\frac{1}{10}$ of the work per day.
• C can complete the work in 15 days. So, C’s rate of work = $\frac{1}{15}$ of the work per day.

Step 2: Determine how much work A, B, and C complete together in 2 days.

The combined rate of A, B, and C when working together: $\text{Combined rate} = \frac{1}{5} + \frac{1}{10} + \frac{1}{15}$ We need to find a common denominator to sum these fractions: $\text{Combined rate} = \frac{6}{30} + \frac{3}{30} + \frac{2}{30} = \frac{11}{30}$ So, together, they complete $\frac{11}{30}$ of the work in 1 day.

In 2 days, they complete: $2 \times \frac{11}{30} = \frac{22}{30} = \frac{11}{15}$ This means that in 2 days, A, B, and C together complete $\frac{11}{15}$ of the total work.

Step 3: Calculate the remaining work.

The total work is 1 unit, so the remaining work after 2 days is: $1 - \frac{11}{15} = \frac{15}{15} - \frac{11}{15} = \frac{4}{15}$ Thus, $\frac{4}{15}$ of the work is still remaining.

Step 4: Calculate the time for C to complete the remaining work.

C’s rate of work is $\frac{1}{15}$ of the work per day. To complete $\frac{4}{15}$ of the work, the time required by C is: $\text{Time} = \frac{4}{15} \div \frac{1}{15} = 4 \text{ days}$

Final Answer:

C will take 4 more days to complete the remaining work after A and B leave.

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Would you like further details on any step?

5 Related Questions:

1. What happens if A, B, and C work together for more than 2 days?
2. How would the time change if B stayed for 1 more day before leaving?
3. Can you calculate the work done by C alone from the start?
4. What if A, B, and C had different work rates, such as 4, 8, and 12 days respectively?
5. How would the total time change if C left instead of A and B?

Tip: When combining rates of work, adding fractions with common denominators helps simplify the process.