there are two trains A and B. which are 30 kms apart.

both the trains are moving towards each other with

velocity of train A is 40 kms / hr

velocity od train B is 60 kms / hr

there is a crow which moves in to and fro motion between the two trains with the speed of 80 kms/hr.

Determine the total distance covered by the crow before it gets crushed between the two trains.

The fly spends the same amount of time traveling as the trains. It goes 80 kms/
hour, so in the 18 min the trains take to collide, the fly will go 24kms.

But The solution above ignores the shape of the fly's path. To picture this
shape, think of the fly as a point made out of rubber. It's bouncing between
the trains at a very high speed. As the trains get closer and closer the
bounces get shorter and shorter, until they are microscopic. Even then, if you
had a strong enough magnifying glass, you could still see the bounces getting
shorter. No matter how much you magnify, there will always be a tinier bounce
that you can't see.

You
can analyze this path by combining the bounces into a series of round trips,
from the first train to the second and back again. It turns out that the length
of each trip is a fraction of the trip before. No matter how many times you
multiply by a fraction, you will never reach zero. The fly makes an infinite
number of round trips, each one smaller than the last.

AL2006 AL2006 · Answer 2 · 2014-08-12T12:57:43-04:00

AL2006 AL2006

12-08-2014

-- If one train covers 40 km per hour and the other one covers 60 km per hour,
then they reduce the gap between them at the rate of 100 km per hour.

-- Since they begin 30 km apart, they meet and crush the crow in 30/100 = 0.3 hour.

-- The crow's speed is 80 km per hour. In 0.3 hour, he covers 0.3 x 80 = 24 km.

Note: 40 km/hr and 60 km/hr are speeds, not velocities.

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