The Train and the Birds Puzzle

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.

1. 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).

2. 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: $$100\text{ mph}\times 1\text{ hour}=100\text{ miles}.$$