Question

When does the sentence "By the time he reached the seventeenth floor, which seemed to take forever, he was winded and gasping?" use dependent, independent, and adjective clauses?

Answer 1

There is one adjective clause in that sentence (which is phrased incorrectly) and one adverbial clause

Almost all adjective clauses start with one of these words: who, which, that, whom, whose (relative pronouns).
http://grammar.ccc.commnet.edu/grammar/clauses.htm#adjective_clauses

All adverbial clauses tell something about WHEN the action of the verb took place. They can start with a wide variety of words.
http://grammar.ccc.commnet.edu/grammar/clauses.htm#adverb_clauses

So ... there are three clauses in that sentence -- the main clause, an adverb clause, and and adjective clause. Can you find them?