1. **State the problem:** You run around the perimeter of a baseball field that consists of a 40% sector of a circle with radius 225 feet plus a straight edge of 300 feet. You run at 9 feet per second. We need to find how long it takes to run around the entire perimeter to the nearest tenth of a second. 2. **Formula for perimeter:** The perimeter $P$ is the sum of the arc length of the sector plus the straight edge. 3. **Calculate the arc length:** The arc length $L$ of a sector is given by $$L = \theta \times r$$ where $\theta$ is the central angle in radians and $r$ is the radius. 4. **Convert 40% of a circle to radians:** A full circle is $2\pi$ radians. 40% of a circle is $$\theta = 0.40 \times 2\pi = 0.8\pi$$ 5. **Calculate arc length:** $$L = 0.8\pi \times 225 = 180\pi$$ 6. **Calculate total perimeter:** $$P = L + 300 = 180\pi + 300$$ 7. **Calculate time:** Time $t$ is distance divided by speed: $$t = \frac{P}{9} = \frac{180\pi + 300}{9}$$ 8. **Simplify the fraction:** $$t = \frac{\cancel{9} \times 20\pi + \cancel{9} \times 33.333...}{\cancel{9}} = 20\pi + 33.333...$$ 9. **Calculate numerical value:** $$t \approx 20 \times 3.1416 + 33.333... = 62.832 + 33.333 = 96.165$$ 10. **Round to nearest tenth:** $$t \approx 96.2 \text{ seconds}$$ **Final answer:** It takes about **96.2 seconds** to run around the baseball field perimeter.