grammaticality - "For how long have you been..." vs. "how long have you been..."

Ante-scriptum: The question should be quite a frequently arising one, so this might be a duplicate. If it is, I haven't found it previously asked here

I don't know if the title is meaningful, but here's the question, anyway. What I want to know is whether the for at the beginning of the following question should be removed or not:

For how long have you been eating?

I consider the sentence to be correct, but some days ago, a teacher (not mine) told me that it was not. And then I remembered that someone else had told me that while it is OK to use the for, the tendency is to get rid of it.

So what's your take on it?