Lets
consider the trains first. The train A is traveling at 40 km/ hour and the
train B is going 60 kms/ hour
So they are approaching each other at (60+40) kms/ hour = 100 kms/ hour.
Distance between them = 30kms
So Distance = Rate * Time
Time
= Distance / Rate
=
(30 km) / (100 kms/ hour)
=
3/10 hour.
=18min
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.
