Breakdown of Благодаря хорошей дороге мы быстро проехали мимо города.
мы
we
город
city
хороший
good
быстро
fast, quickly
Questions & Answers about Благодаря хорошей дороге мы быстро проехали мимо города.
Why do we need the preposition мимо here if the verb проехали already implies driving past something?
While the prefix про- in проехали indicates moving past or through an area, it doesn't specify exactly how. Using мимо plus the Genitive case (города) makes it completely clear that you drove past the outside of the city, rather than straight through the middle of it.
Why is хорошей дороге in the Dative case here?
Because of the word Благодаря (thanks to). Even though it comes from a verb, it acts as a preposition here and always requires the Dative case. That is why the Nominative phrase хорошая дорога changes to хорошей дороге.
Could I just say ехали мимо города instead of проехали?
You could, but it changes the focus from a completed action to an ongoing process. мы ехали мимо means we were in the process of driving past, while the perfective verb проехали shows that you successfully finished passing the city and left it behind.
Is the word order strict? Could быстро go somewhere else?
Russian word order is quite flexible. You could put быстро after the verb or even at the end of the sentence. However, placing the adverb right before the verb it describes, as in быстро проехали, is the most standard and natural way to express this.