Question

Locate the subordinate clause in the following sentence, and identify it as a noun, adjective, or adverb.

Answer 1

Who just finished the marathon is tired is the subordinate clause, because it started with a relative pronoun, it is classified as a relative clause. "Just" is the subordinate conjunction and it is an adverb because it modifies the "finished" in the sentence to show immediacy. 

Answer 2

The subordinate clause in this example is 'who just finished the marathon', because it cannot exist on its own - you cannot write just this clause and put a full stop, because the clause is not completed, it needs to be a part of a larger, main, independent clause. That is why it is subordinate.
As for the type of the clause, this is an 'adjective clause', because it modifies, or refers to 'the woman', she is the one who just finished the marathon and that is why she is tired. It describes the subject in more detail, and that is exactly the function of an adjective, or adjective clause.