1. **Problem statement:** Two trains start at 10:00 am from stations 200 miles apart, traveling towards each other at 100 mph each. A vulture flies back and forth between the trains at 200 mph until the trains meet at 11:00 am. We need to find how many miles the vulture flies before the trains meet. 2. **Key information:** - Distance between stations: 200 miles - Speed of each train: 100 mph - Speed of vulture: 200 mph - Time until trains meet: 1 hour (from 10:00 am to 11:00 am) 3. **Step 1: Calculate the time until trains meet.** Since both trains travel towards each other at 100 mph, their combined speed is: $$100 + 100 = 200 \text{ mph}$$ Distance between them is 200 miles, so time to meet is: $$\text{time} = \frac{\text{distance}}{\text{combined speed}} = \frac{200}{200} = 1 \text{ hour}$$ 4. **Step 2: Calculate how far the vulture flies.** The vulture flies continuously for the entire 1 hour at 200 mph, so the total distance flown is: $$\text{distance} = \text{speed} \times \text{time} = 200 \times 1 = 200 \text{ miles}$$ 5. **Answer:** The vulture flies **200 miles** before the trains meet.