Two trains are on the same railroad track separated by 200 miles and facing towa

Question

Two trains are on the same railroad track separated by 200 miles and facing towards each other. Train A is moving at 50 mph while Train B is moving at 100 miles per hour. At that instant a very fast flying bird that flies at a rate of 125 mph takes off from the tip of Train A and flies directly towards Train B, which it just reaches, then turns around instantly and flies back towards Train A, then turns around upon reaching Train A and flies back to Train B, repeating this process until the two trains collide. How far does the bird fly in total?

Explanation / Answer

speed of bird = 125 mph

speed of train A v1 = 50 mph

speed of train B v2 = 100 mph

Distance between train A and B = 200 miles

relative velocity = 50+100 =150 mph (because both are in opposite direction)

Time taken by trains when collide t = d/v =200/150 = 4/3 hr

So distance travelled by bird = ( speed of bird)* t

= 125*4/3 =500/3 =133.33 miles

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