frequency with which

I'd stick with with which there.

Both are acceptable. Probably I would choose "with".

By the way, what do you mean by "cut path"? I wonder whether this is the best term, but I am not sure what sort of situation you are referring to.

(Cross-posted.)

Thanks

What about:

...the pace with/at which you are learning.
...the pace with/at which you walking.
...the rate with/at which the world is changing.

What's the rule that I could use to determine whether I should use which or at in sentences like these?

... the pace at which you are learning.
... the pace at which you are walking.
... the rate at which the world is changing.

MustAskWhat's the rule that I could use to determine whether I should use which or at in sentences like these?

You can simplify the question by removing the relative clause:

GPYBeyond that, you just have to figure out, from the meanings of the prepositions, or from a knowledge of set idiomatic patterns, which preposition fits. Unfortunately, with prepositions, it does often come down to learning the set patterns of usage.

Yes, this is at times difficult.

To get a better feel for it, what would you say in the following:

MustAsk... the speed at/with which the whole situation went down...

You may see both of those used. I think "at" is more proper. Others may differ.