Based on the clauses provided, here's how they should be categorized:
Independent Clause:
- she drove from Washington, DC, to New York
- my friend Tim teaches at the local business college
Dependent Clause:
- after I finish my homework
- since Adam likes to play soccer
Independent clauses can stand alone as complete sentences, while dependent clauses cannot stand alone and are usually introduced by subordinating conjunctions (like "after" and "since").