The train

“Have you noticed anything about this train, Son?”

“Like what, Dad?”

“Well. We’ve been stood here now for what…”

“About three hours, I should think.”

“Right; about three hours. And how many times have we seen this tourist train thin pass us?”

“This is the twelfth time, Dad. It’s quite regular. Passes every thirty minutes, give or take a few seconds. And within six minutes of passing us on the way down, it passes us again on the way back.”

“Ah, but there’s the question, Lad. On its way from where to where?”

“And back again.”

“And back again, but where?”

“I think you’ll find that it turns at a point down the road from us. Depending on how long it stops before turning back – let’s say it stops for two minutes – I would estimate its turning point to be two minutes down the road.”

“But that doesn’t tell us where it turns, does it? It only tells us how long.”

“Bear with, Dad. Given that its speed over its course is relatively constant—”

“Relatively constant? That’s an oxymoron, like ‘civil engineer’ and ‘military intelligence’.”

“Okay, let’s assume that its speed is steady, within plus or minus ten percent of its average—”

“That’s better. But what is its average speed?”

“According to my watch, the distance from the beginning of this range of buildings to where we are now is exactly 134 metres, which over the last eleven trips it has covered in an average of 24 seconds, giving a speed of 5.583 metres per second or 20.1 kph. Given that it does the return journey in 6 minutes—”

“With a stop of indeterminate length.”

“I have stipulated a stop of indeterminate length. That means that its turning point is between 670 metres and one kilometre from our current position.”

“And its point of origin?”

“I’ve assumed a longer stop at its origin, say five minutes. Its turn-round time from our position would thus be nineteen minutes, giving an origin nine and a half minutes drive from here. At an average of 20kph, that implies a distance of… nine point five times sixty, or five hundred and seventy seconds. At a rate of five point eight three recurring metres per second, a distance of three point three two five kilometres is suggested.”


“Yes, Dad. There are too many assumptions to be more positive than that.”

“Can I put another question to you, Son?”

“I’d love you to, Dad.”

“Well. We’re on holiday here, right?”


“And the purpose of this holiday is?”

“Ah! I know this one. It’s to encourage me to relax and not fixate on anything.”

“And to have some fun. That’s what I thought, too.”

“Well, it’s working, isn’t it?”

“We’ve been standing on this same spot for three hours, just watching a train go by.”

“I know. It’s great.”

“Is it?”

“I’m not sure I understand what you’re trying to say, Dad. I’ve never been more relaxed; I’m watching a train and I get to do some calculations. What could be better?”

“Oh, let me see if I can think of something: maybe having a drink in a bar or a snack in a restaurant? Or what about looking around some of these gift shops, or even one of the ancient religious buildings?”

“Oh, Dad, have you listened to yourself? How can any of that be more fun than what we’re doing now?”

“You’re really enjoying this?”

“There’s only one thing could make this day more perfect than it already is.”

“And what’s that?”

“Can I drive the train, Dad; can I? Oh, do ask the man if I can; pleeeease.”

I wrote this in response to Kreative Kue 172, issued on this site earlier this week. Feel free to join in; just follow the link.

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