1. **State the problem:** We need to find the total distance traveled by the train given its speed over time as a piecewise linear function. 2. **Understand the problem:** Distance traveled is the area under the speed-time graph. Since speed is in miles/hr and time in hours, the area under the curve gives distance in miles. 3. **Analyze the graph:** The speed increases linearly from 0 to 60 miles/hr in the first hour, stays constant at 60 miles/hr from 1 to 9 hours, then decreases linearly from 60 miles/hr to 0 in the last hour (9 to 10 hours). 4. **Break the graph into sections:** - Section 1 (0 to 1 hr): Speed increases linearly from 0 to 60. - Section 2 (1 to 9 hr): Speed is constant at 60. - Section 3 (9 to 10 hr): Speed decreases linearly from 60 to 0. 5. **Calculate area for each section:** - Section 1 is a triangle with base 1 hr and height 60 miles/hr: $$\text{Area}_1 = \frac{1}{2} \times 1 \times 60 = 30$$ miles - Section 2 is a rectangle with width 8 hr and height 60 miles/hr: $$\text{Area}_2 = 8 \times 60 = 480$$ miles - Section 3 is a triangle with base 1 hr and height 60 miles/hr: $$\text{Area}_3 = \frac{1}{2} \times 1 \times 60 = 30$$ miles 6. **Sum all areas to find total distance:** $$\text{Total distance} = 30 + 480 + 30 = 540$$ miles 7. **Final answer:** The train travels **540 miles**.