You had ~2250 visits that day (1440 minutes), each of which spent (on average) ~45 minutes looking at your website. Assuming only one concurrent visitor, you'd have had 1440/45 = 32 total visits. You actually had 2250/32 = ~70 times that number, so you averaged ~70 concurrent visits that day.
Due to expected fluctuations (day/night, when you posted to HN) there will be considerable real-time variation; it is easy to believe that you spiked up to 282 concurrent visitors at some point when people were heavily commenting on HN: however, the real question here is what the concurrent number of requests looked like.
Finally, yes: one way to look at these visitors is that they were "spread out over 45 minutes" (although that isn't how I'd describe it myself). If you asked "during any given 45 minute period, how many visits (on average) started during that period", we would be looking at 2250/(1440/45), or ~70 visits starting in that window.
Due to expected fluctuations (day/night, when you posted to HN) there will be considerable real-time variation; it is easy to believe that you spiked up to 282 concurrent visitors at some point when people were heavily commenting on HN: however, the real question here is what the concurrent number of requests looked like.
Finally, yes: one way to look at these visitors is that they were "spread out over 45 minutes" (although that isn't how I'd describe it myself). If you asked "during any given 45 minute period, how many visits (on average) started during that period", we would be looking at 2250/(1440/45), or ~70 visits starting in that window.