I'll answer in reverse order.
I think what you suggest works! Putting it in the wording of my original comment: Mary IS 24, Ann WAS 12, and the same amount of time gets you from 12 to Ann's current age, and from Ann's current age to 24. I think it is obvious from there that you're half-way between, so Ann is 18. Thank you!
The part of your earlier comment I consider gibberish has nothing to do with the problem.
> It's slightly different, because you've supercharged your hammer.
This does not mean anything.
> Everything you ever understood about how to solve word problems has been subsumed into what your brain labels as "algebra."
This is bizarre speculation. Why are you analyzing my brain? I just asked for an explanation!
> Did you use algebra to convert the problem to algebraic form?
As you say, this is impossible to do, because it doesn't make sense. So why bring it up? It sounds like you are trying to convince me the problem is not algebra - or that I am in some way only seeing it as algebra because I am not thinking about the problem clearly. But I never said it was! I just said I can't see how to do it without algebra. Since you mixed those things up, I clarified by saying exactly what sense I was talking about algebra in the first place. Clearly that didn't work!
Again, thank you for explaining your reasoning, I appreciate it. Just leave out the analysis of my mind!