1. **State the problem:** Akira and Taro biked a total of 276 miles after two weeks and 413 miles after three weeks. We need to find how many miles they biked in the third week. 2. **Identify the formula:** The total miles after three weeks equals the total miles after two weeks plus the miles biked in the third week. 3. **Set up the equation:** Let $x$ be the miles biked in the third week. $$276 + x = 413$$ 4. **Solve for $x$:** $$x = 413 - 276$$ 5. **Calculate the difference:** $$x = 137$$ 6. **Answer:** Akira and Taro biked 137 miles in the third week.