Two trains travel toward each other on the same track, beginning 100 miles apart. one train travels at 40 miles per hour; the other travels at 60 miles an hour. a bird starts flight at the same location as the faster train, flying at a speed of 90 miles per hour. when it reaches the slower train, it turns around, flying the other direction at the same speed. when it reaches the fastest train again, it turns around -- and so on. when the trains collide, how many miles the bird has flown.

-- One train travels at 60 mph.  The other one travels at 40 mph.  So the space between them shrinks at the rate of 100 mph.

-- They start 100 miles apart, so they meet in 1 hour.

-- The bird and the trains all start moving at the same time, and the bird keeps flying in the space between them until they meet.  That's 1 hour.

-- The bird's speed is 90 mph.  So the bird covers 90 miles in that hour.

-- After flying at 90 mph for a whole hour without resting, we can be sure that the bird is grateful to be put out of its misery.

where are the vectors ?

it would be kevlar ^^