Answer and Explanation:
There are two sentences in this question. Let's analyze them separately.
When the clock chimed three, the school bell rang, and the children raced to the bus.
Independent clauses: the school bell rang, and the children raced to the bus. ("and" is a coordinating conjunction)
Subordinate clause: When the clock chimed three ("when" is a subordinating conjunction)
Therefore, what we have here is a compound-complex sentence - formed by two independent clauses and a dependent/subordinate one, at least.
The Northwest is damp and rainy, but the Southwest is dry.
Independent clauses: The Northwest is damp and rainy, but the Southwest is dry. ("but" is a coordinating conjunction)
Subordinate clauses: none
Here, we have a compound sentence - formed by joining two independent clauses connected by a coordinating conjunction - for, and, nor, but, or, yet, so.