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This sentence deals with distance, Curious. The reason that A is correct is that these words deal with distance.
We don't normally use much or more when referring to distance. Yes, theoretically I could ask you, "How much did you walk today?" but it doesn't sound natural. I'm much more likely to ask you, "How far did you walk today?" if I'm thinking about distance, or "How long did you walk today?" if I'm thinking about how much time you put into that activity.