1. **State the problem:** Riley and Anthony run around a semi-circular curve. Riley runs on the inside lane with radius $35$ meters, and Anthony runs on the outside lane with radius $42.5$ meters. We need to find how much farther Anthony runs compared to Riley when they complete the curve. 2. **Formula used:** The length of a semi-circular path is half the circumference of a circle. The circumference of a circle is given by $$C = 2\pi r$$ so the length of a semi-circle is $$L = \pi r$$. 3. **Calculate Riley's distance:** $$L_{Riley} = \pi \times 35 = 35\pi$$ meters. 4. **Calculate Anthony's distance:** $$L_{Anthony} = \pi \times 42.5 = 42.5\pi$$ meters. 5. **Find the difference:** $$\text{Difference} = L_{Anthony} - L_{Riley} = 42.5\pi - 35\pi = (42.5 - 35)\pi = 7.5\pi$$ meters. 6. **Evaluate the difference numerically:** $$7.5\pi \approx 7.5 \times 3.1416 = 23.56$$ meters. **Answer:** Anthony runs approximately $23.56$ meters farther than Riley around the curve.