1. **Stating the problem:** We have a race track with three cones placed along a line: two black cones and one white cone exactly in the middle between the two black cones. The distances given are 206.25 m and 271.14 m, which likely represent the distances from the start to the cones. 2. **Understanding the setup:** The white cone is exactly in the middle of the two black cones. This means the position of the white cone is the midpoint between the two black cones. 3. **Formula for midpoint:** If the positions of the two black cones are $x_1$ and $x_2$, then the white cone position $x_w$ is given by: $$x_w = \frac{x_1 + x_2}{2}$$ 4. **Assigning values:** Let's assume the first black cone is at 206.25 m and the second black cone is at 271.14 m. 5. **Calculate the midpoint:** $$x_w = \frac{206.25 + 271.14}{2} = \frac{477.39}{2} = 238.695$$ 6. **Interpretation:** The white cone is located at 238.695 m from the start, exactly halfway between the two black cones. **Final answer:** The white cone is at $238.695$ meters from the start.