Truth be told, I wouldn't use either "rather" or "relatively". If you want to emphasize that it is not just late, it is too late then you can say so. "Rather" is not a word of choice because it is used to "blur the boundaries" of the word it modifies.
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Thinking SpainCould it be right according to the context?Yes, in fact that's the kind of context that occurred to me when I read your original question. Still, I wouldn't try to make too fine a distinction between the two and I don't think you should try to generalize this situation, it is after all a very specific context.
FandorinAnother example is ok, but "not having" is out of place. While it is still grammatically correct, the wording seems odd to me.Hi,