Friday, August 30, 2013

Bird Running Between Trains - Classic Puzzle

It is a classic Puzzle. And it can be seen all over the internet.

A train leaves City X for City Y at 15 mph. Same instant, another train leaves City Y for City X at 20 mph on the same track. (There will be an accident. Huh...)

At the same moment, there is a bird that was sitting on the engine of train at city X. It leaves the train and flies towards the City Y train  at 25 mph. When the bird reaches the train from City Y, it immediately reverses its direction.

It then continues to fly at the same speed towards the train from City X, when it reverses its direction again, and so forth. The bird continues to do this until the trains collide. How far would the bird have traveled in the entire to and fro journey.

2 comments:

  1. I think distance between city X and city Y should be given.

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  2. i am giving a probable solution. Better is left for audience to solve, or else what will be the puzzle the. Hehe :)

    The concept of relative speed (rings a bell?) can work handy here. Let’s assume that the distance between City X and City Y is d miles. The trains are approaching each other at a relative speed of (20 + 15) = 35 mph. The sum of the distances covered by the trains when they collide is d (i.e. the distance between the cities). Since distance/speed gives us time, we know that the trains collide d/35 hours after they start.

    Since the speed of the bird is constant at 25 mph, we know that the bird would have covered

    25 * (d/35) miles = 5d/7 miles

    before the trains collide.

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