## Monday, February 15, 2010

### One fly and two colliding trains.

Two trains are running one against the other at 50 km/h each. They are 100Km far away. Soon they will collide. One fly is flying from one train to another, first it moves in one direction and as soon as it touches one train it flyies back in the other direction. The fly has a 30Km/h speed. How much space will the fly cover?

1. If the arithmetic data are correct, then the trains will collide before the fly reaches the first train.
That is beacuse both trains travel faster thn the fly.
To compute the distance that the fly covers we need to
find when the trains will collide.
This is after 1 hour. Within this time perid, the fly will cover 30km.

PS. Another interesting approach is to use Zeno's paradox. In a similar occassion, Zeno proves that the trains will NEVER collide. Hence, the fly will cover infinite space.

2. Ans : 30km
Since two trains are against each other, the net speed is 100km/h. The distance is 100 km. So It takes 1 hour for them to collide. OTOH the fly could travel 30 km in 1 hour

3. The fly is slower than a train, so once it touches a train, the fly is stuck to that train.
It will fly at 30km/h until it reach a train, and then at 50km/h until the collision.
The space covered by the fly varies from 30km to 50km, depending on its initial position: 50km if it started "on a train", 30km if it started in a position such that it will be exactely between the trains when they collide (so 30km away from the middle).