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The actual answer would be fairly difficult to calculate. I guess see how much you can mine in five minutes, divide 4000 by that, then multiply by five. Hey presto, total time in minutes.
Remember that the fastest mining speed involves dual-wielding + elemental fury + other relevant perks.
We know that for every 3 hits, we obtain a resource drop. Every resource drop obtains 4 R (R = Resource). We would need 1000 resource drops to obtain all 4000 R. So 3000 hits = 4000 R.
1000 Resource Drops, 3000 Hits = 4000 Resources.
Looking over my recordings, I can see that the starting 3 hits (starting the animation takes longer than continuous hits) takes 5 seconds (rounded down). Then, the next 3 looped hits take 4 seconds (4.10, rounded down.)
1st Resource Drop= 5 seconds.
2 - 1000 Resource Drops= 4 seconds.
So 999 x 4 = 3996 seconds + 5 = 4001 Seconds. Lets say a resource per second. So a minute is 60 resources. An hour would be 60 x 60 = 3600.
1 second = 1 resource.
4001 seconds = 4000 resources.
1 minute = 60 resources.
1 hour = 3600 resources.
To obtain every single resource, it would take 66.68333 minutes (4001 seconds to minutes). Pretty much 67 minutes, an hour and 7 minutes.
SOLVED BY MATH: To obtain all 4000 resources, it would take 67 minutes.
Now unless I'm stupid or I did something wrong, this should be correct.