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Train from Copenhagen to Hamburg goes from 4.5 to 2.5 hours. As a Swede, this makes vacations to the continent via car or train much more attractive.

That sounds really nice! I wish we had train network in the US. Though I get the country is huge but so is Europe from tip to tip.

You do. It's just not used for PAX, besides a few exceptions. Look for Class 1 Railroad on Wikipedia, and compare freight to passenger trackage.