[mohn]

Interesting question, a lot of search engine results claim that John Von Neumann was presented with the problem and quickly solved it by summing the infinite series instead reframing it as a constant speed for an easily calculated duration. Plausible, but sounds apocryphal. Here's the oldest reference I've found and verified by reading scans[0] of the source book:

Initiation Mathématique (1906) by Charles-Ange Laisant (1841--1920), number 53. Le chien et les deux voyageurs.

The setup here has two pedestrians walking in the same direction with a dog running back and forth between them. One of them starts out some distance ahead of the other but, because the one behind walks faster, they eventually intersect. It briefly mentions a variation where they are walking toward one another, as in the typical trains & fly version of the problem. Best of luck finding older, I wouldn't be surprised if it's out there!

[0]: https://i.imgur.com/vCCFgAQ.png

[mohn]

Whoops, my comment was supposed to say "instead of reframing", but the crucial "of" got lost when I reworded things. Too late to edit now.

[arjie]

Very cool! Thank you for doing the research to get that far!

[lukasec]

Great find! plan to add these variants to our parameter sampling. First time I saw this problem was when my game theory prof told this story. It's definitely folklore (see The Legend of John von Neumann by Halmos)