The mistake in the first sentence provided is the adjective quick. The correct word in that place of the sentence should be quickly, which is an adverb, due to the fact that adverbs modify verbs, and adjectives (quick) modify nouns. In this case, quickly refers to the action of the sentence of working quickly. So, that quickly modifies the verb "work."
In the second sentence there is no mistake. Every single type of word is well placed to convey the meaning.