Henry Ernest Dudeney/Puzzles and Curious Problems/66 - Meeting Trains/Solution

by : $66$

 * Meeting Trains

Solution

 * $9$ trains.

Proof
Let $W$ and $M$ denote Wurzeltown and Mudville respectively.

Each train takes $5$ hours for the journey.

At the point of departure from $W$, there will be:
 * $1$ train just arriving at $W$ from $M$
 * $1$ train just starting out from $M$
 * Another $4$ trains already in transit from $M$ to $W$.

During the course of the journey from $W$ to $M$, $4$ more trains start off from $M$ to $W$.

At the arrival at $M$, another train is just about to leave $M$ for $W$.

So, not counting the two trains at either end (just arriving at $W$ and just about to leave $M$), there are $9$ trains met along the way.