The bird travels 100 miles before the trains collide.
Explanation:
Instead of calculating each individual leg of the bird’s flight, let’s take a simpler approach using time.
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Time until collision:
- The two trains are 50 miles apart, moving toward each other at 25 mph each.
- Their combined closing speed is 25 mph + 25 mph = 50 mph.
- Since they are 50 miles apart, they will collide in 1 hour (50 miles ÷ 50 mph = 1 hour).
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Distance traveled by the bird:
- The bird flies at 100 mph for the entire 1 hour before the trains collide.
- Since speed × time = distance, the bird travels: 100 mph×1 hour=100 miles.100 \text{ mph} \times 1 \text{ hour} = 100 \text{ miles}.100 mph×1 hour=100 miles.