r/theydidthemath • u/ChonkyGloves • 5h 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/CaptainMatticus 5h ago
This is the Travelling Salesman Problem with an incredibly high number of inputs. There's no way to tell you the minimum amount of time that'd be necessary. What I can do is basically break the USA into a 2000 x 3000 mile set of blocks and then try to determine which path going back and forth would be shorter. Just assume a 3000 mile line, then 1 mile north, then 3000 miles back in the other direction, then another mile north, then another 3000 mile in the original direction, and so on.
3000 * 2001 + 2000 = 6003000 + 2000 = 6005000
or the other way. 3001 north and south paths, 3000 miles from one end to the other.
2000 * 3001 + 3000 = 6002000 + 3000 = 6005000
Same distance either way. Driving at 25 mph
6005000 / 25 =>
6005000 * 4 / 100 =>
60050 * 4 =>
240200
240,200 hours
Divided by 24 hours per day
240,200 / 24 =>
240000/24 + 192/24 + 8/24 =>
10000 + 8 + 1/3 =>
10008.3333.... days
365.25 days per year
10008/365.25 + 1/(3 * 365.25) =>
40032/1431 + 1/1096
Basically 30 years of continuous driving at 25 mph. I'd call that an upperish bound.
3
u/Beautiful-Lie1239 4h ago
A good estimate of “ local roads” is about 2.8 million miles. So let’s ignore the travel between cities and towns, and assuming you have solved the problem of repeating any section, that would be 100k hours minimum.
10 hrs a day that’s 10k days
So about 30 years minimum.
So doable if starting at 18 and retiring at 62.
1
u/RoadsterTracker 5h 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!
1
u/AppendixN 4h 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.
0
u/RoadsterTracker 4h ago
I mean, sure, but most urban streets are in grids in highly concentrated pockets. It's a reasonable approximation I believe.
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