Two trains travel directly toward each other. One of the trains travels at a rate of 12 km/h while the other travels at a rate of 20 km/h. When the trains are 72 km apart a conductor at the front of one of the trains releases the insane pigeon Hyde. Hyde flies first from the slower of the two trains to the faster train at which point Hyde doubles back toward the slower train. Hyde continues to fly back and forth between the trains as they approach, always at a constant speed of 48 km/h. Assuming the trains never change speed until they meet and magically stop, how many kilometers has Hyde flown when the trains meet?
Maybe this question is easier than it looks.
One train is traveling at 12km/hr and the other is traveling at 20km/hour in the opposite direction.
If you are a passenger sitting inside the train it appears like you are stopped and everything outside the train is moving.
The train you are NOT on has the relative speed of 12+20=32km/hour
So I think the senario is similar to a magical soft brick wall and a train that is at an instant 72 km away traveling towards it at 32km/hour.
we have distance and speed so t = d/s = 72/32 = 2.25 hours.
The two trains will collide very gently in 2.25 hours.
All this time poor crazy hyde is flying. So he flies at 48km/hour for 2.25 hours
distance he has travelled is s*t = 48*2.25 = 108km.