Explanation:

- A can complete the task alone in 80 days.

- A works for 10 days, doing \( \frac{10}{80} = \frac{1}{8} \) of the work.

- Remaining work is \( 1 - \frac{1}{8} = \frac{7}{8} \).

- B finishes \( \frac{7}{8} \) of the work in 42 days.

- Hence, B can complete the entire work in \( \frac{42}{\frac{7}{8}} = 48 \) days.

- A's work rate is \( \frac{1}{80} \) of the work per day.

- B's work rate is \( \frac{1}{48} \) of the work per day.

- Combined work rate of A and B is \( \frac{1}{80} + \frac{1}{48} \).

- Simplifying this gives \( \frac{1}{30} \) of the work per day.

- Therefore, together, A and B can finish the work in 30 days.

- Answer: 30 days