The Train and the Birds Puzzle

Two trains are 50 miles apart, traveling toward each other at 25 miles per hour each. A bird starts flying from the front of one train at 100 miles per hour, flying back and forth between the two trains until they collide. How far does the bird travel before the collision?

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 mph×1 hour=100 miles.100 \text{ mph} \times 1 \text{ hour} = 100 \text{ miles}.
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