Learn Finnish: Tietä korjattaessa täytyy käyttää kiertotietä. - When the road is being repaired, you must use the detour.

This is the passive temporal construction. You form it by taking the passive past participle (korjattu), changing the final -u or -y to an -a or -ä to get the stem (korjatta-), and then adding the inessive ending -essa or -essä.

Why is tietä in the partitive case?

Tietä is the object of the passive temporal construction (korjattaessa). A strict rule in Finnish grammar is that the object of a passive temporal construction must always be in the partitive case, even if it refers to a whole, specific thing.

The English translation says "you must use", but there is no word for "you" in the Finnish sentence. Why?

The sentence uses the necessity verb täytyy (must) without a genitive subject (like sinun). This creates a generic sentence (sometimes called the zero person). It means "one must use" or "people in general must use" the detour.

Why is kiertotietä (detour) also in the partitive case?

It is the object of the verb käyttää (to use). Käyttää is a partitive verb, which means its object almost always takes the partitive case, regardless of whether the sentence is a necessity structure or not.