- John ate and drank to his satisfaction.
- John ate the yam and drank the juice.
My question: Are these sentences simple or compound sentences?
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 John [ate] and [drank] to his satisfaction.
 John [ate the yam] and [drank the juice]
Grammarians don't often talk of simple or compound (or complex) sentences, since many sentences do not fit into one category or the other.
However, since neither example contains subordination and each example consists of a single main clause, I suppose they would be called 'simple' sentences.
What I can tell you, though, is that they are both coordinate constructions. In 1. the coordination consists of the two VPs "ate" + "drank", and in 2. it consists of the two VPs "ate the yam" + "drank the juice".