1. **Problem Statement:** Two trains start from stations 200 miles apart at 10:00 am, traveling towards each other at 100 mph each. A vulture flies back and forth between the trains at 200 mph until they meet at 11:00 am. Find the total distance the vulture flies. 2. **Formula and Important Rules:** - The trains meet after time $t$ hours, where $t$ is the time it takes for the trains to cover 200 miles together. - Since both trains travel towards each other, their relative speed is the sum of their speeds. - Distance = Speed \times Time. 3. **Calculate the time until the trains meet:** - Combined speed of trains = $100 + 100 = 200$ mph. - Distance between stations = 200 miles. - Time until meeting: $$t = \frac{\text{Distance}}{\text{Combined speed}} = \frac{200}{200} = 1 \text{ hour}.$$ 4. **Calculate the distance the vulture flies:** - The vulture flies continuously at 200 mph for the entire time the trains are moving towards each other. - Distance flown by vulture: $$\text{Distance} = \text{Speed} \times \text{Time} = 200 \times 1 = 200 \text{ miles}.$$ **Final Answer:** The vulture flies 200 miles before the trains meet.