Steam Train Showtime (Oct. 2025 Challenge Question)

10 seconds.

There are (at least) two simple ways to think about this.

1.) From a stationary observer's point of view, at the point where the engines meet: both trains are the same length, and, doing the same speed; so their back ends will both pass the observer at the same time, so, you only need to work out how long it will take either train to pass the same point; a sixth of a mile at one mile per minute.

2.) From the point of view of the trains: they have to go twice the length of one train relative to each other at a relative speed of twice their individual speeds: one third of a mile at one mile every thirty seconds.