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?
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?