A puzzle I came up with: The Ferry Problem.

A boat moves people between two islands. Every time a customer arrives at either dock, the boat is alerted. The boat can be either stationary or travel at a fixed velocity between the two islands, and can turn back whenever. If it never stops, it completes the journey from one island to the other in 15 minutes.

If people arrive randomly at either dock at an average rate of once per hour, what is their expected travel + wait time, if the boat follows the optimal strategy to minimize it?

Resolves to correct interval when I can be bothered to figure it out.

• Update 2025-09-19 (PST) (AI summary of creator comment): - Passenger arrivals at either dock follow a Poisson process with average rate 1/hour.

  • Multiple arrivals can occur within any hour; interarrival times are exponential.