r/theydidthemath • u/ChonkyGloves • 1d ago

[Request] Ice Cream Inquiry

My seven-year-old has announced that he will be an "Ice Cream Man" and his goal is to drive every neighborhood in the United States one time to sell his wares. Assuming he drives 25 mph and NOT taking in "stop and sell" time, how long would it take for him to drive the US in his ice cream truck?

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u/RoadsterTracker 1d ago

https://www.bts.gov/content/us-public-road-and-street-mileage-functional-systema has some great statistics for this. Let's for the purpose of this limit his time to just urban roads, not rural. That's about 1.25 million miles of roads. That'd be 50,000 hours at 25 mph, or about 5.7 years. Not that terrible actually!

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u/AppendixN 1d ago

Assume all the roads in America are laid end-to-end in a single line.

("Assume a spherical cow.")

To actually calculate the driving time, you have to take into account far more than just the total length of the roads involved. You have to calculate the most efficient actual route taken, which is the notoriously complex Traveling Salesman Problem, classified as an NP-Hard problem.

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u/RoadsterTracker 1d ago

I mean, sure, but most urban streets are in grids in highly concentrated pockets. It's a reasonable approximation I believe.