I translated it as: By being silent, I ate more quickly and was told that quicker should have been used in place of more quickly.

"Quicker is the comparative of quick, which is an adjective; more quickly is the comparative of quickly, which is an adverb."

The problem may arise because "While faster is and can be used as both an adverb and and adjective, quicker can be used only as an adjective."

At any rate quicker is wrong, faster is right, and more quickly should be right.

The Duolingo robot does not seem to like "more quickly", but it is perfectly standard English. Could it be added, please?

If the pronouns are missing I think that "Being silent, WE ate faster" is also correct.