Well, here's my work:
if I take 1 hour to travel 500m, then I'm travelling 500m/hour
In order to travel 1k/hour, I'll have to have travelled the last 500m already as well
Since that's impossible, I'll instead take an infinite amount of time to travel the first 500m. Which means it should be pretty simple to go the last 500m in the same amount of time, since infinity divided by 2 is still infinity.
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