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I'm having trouble with the translation to Latin (III. Sentence 1)

How many days after me do you want to set out to Rome?

M&F have previously given us quantus - how much, how great, and quot - how many. I took from this that if you were referring to countable things you used quot, and for, well.....quantities that had to be measured, you used quantus.
However, M&F's translation into Latin is

Quantīs diēbus post mē Rōmam proficīscī vīs?

which I can follow, but clearly goes against what I thought. So what is the distinction between quot and quantus? And is the literal translation "post me" quite kosher here? I thought you might have to use a verbal form, like "after I leave" or "after my leaving" (as in the way they said "yes").