Declination of adjective

Question

In the following sentence:

Ihr habt lange darauf gewartet.

For the adjective "lange", what is the declination in this case? Here we don't have defined or undefined articles so by the position I would say it should be accusative but then we have two possibilities: feminine and plural (declination with no article). Why should "darauf" be feminine or why should it be plural? Do I need the whole context to be able to point out the gender of what it is meant by "darauf"?

Answer 1

In fact, lange is an adverb here, and therefore requires no declension. Darauf is not a noun, but rather a prepositional phrase. The sentence means, roughly,

You have been waiting for that for a long time.

Answer 2

In this sentence, lange is an adverb describing the verb warten and as such is not declined at all.

darauf is a preposition. Prepositions have no gender and are neither singular nor plural.