Matching Tenses

I remember Mrs. Baird, my high school English teacher, mentioning this topic, but she didn’t go into detail, and I can’t at the moment conjure up a set of rules about this beyond the extremely generic statement that verb tenses should not conflict when you have more than one verb in a sentence.

This sentence from a hearing aid newsletter reminded me of this.

Prepare in advance and have spares on you in case something is lost or runs out of power before you expected.

That should be “expect,” present tense like the rest of the sentence.

I ran into a question on Quora that raises this issue:

“The irony is that it would have been faster to “have taken”/“take” the back roads after all.” Is there a difference between “to take” and “to have taken” in this example?

The answer is that the sentence should use “have taken” because the tense matches “have been faster.”

Do any of you have a more formal explanation of why this is so?