1. **State the problem:** John drives south for 8 miles, then east for 15 miles, and returns home by a straight road. We need to find the total distance he drives after 7 days. 2. **Identify the formula:** The straight road back home forms the hypotenuse of a right triangle with legs 8 miles and 15 miles. Use the Pythagorean theorem: $$c = \sqrt{a^2 + b^2}$$ where $a=8$ miles and $b=15$ miles. 3. **Calculate the hypotenuse:** $$c = \sqrt{8^2 + 15^2} = \sqrt{64 + 225} = \sqrt{289} = 17$$ miles. 4. **Calculate total distance for one day:** John drives 8 miles + 15 miles + 17 miles = $8 + 15 + 17 = 40$ miles per day. 5. **Calculate total distance for 7 days:** $$7 \times 40 = 280$$ miles. **Final answer:** John drives a total of 280 miles after 7 days.