Learn Polish: Tłumacz ślęczał nad tekstem całe popołudnie, chociaż był zmęczony. - The translator pored over the text the whole afternoon, although he was tired.

This is the bare Accusative of continuous extent. In Polish, when you want to express how long an ongoing action lasted (like "the whole afternoon"), you can put the time phrase directly into the Accusative case. No preposition is strictly needed, though you could also say przez całe popołudnie with the exact same meaning.

Why is ślęczał in the imperfective aspect?

The phrase całe popołudnie emphasizes the continuous, ongoing duration of the action. Imperfective verbs are naturally used to describe the ongoing process of an action over a period of time, regardless of whether the translator eventually finished the text.

Why does ślęczał take the preposition nad with the Instrumental case (tekstem)?

The verb ślęczeć means "to pore over" or "to slave away at" something. Just like leaning physically over a desk, it takes the preposition nad (over). Because nad here describes a static, ongoing situation rather than motion to a new destination, it requires the noun to be in the Instrumental case.

Why is zmęczony in the Nominative case rather than the Instrumental after the verb był?