Learn Hardcore Russian: Мы решаем проблему вместе.

Because проблема is the subject form (nominative), but here it’s the direct object of решаем, so it takes the accusative case. For most singular feminine nouns ending in -а, the accusative ending is -у, turning проблема into проблему.

Why is the verb решаем in the imperfective aspect rather than the perfective?

Russian has two aspects: imperfective describes ongoing or repeated actions, perfective describes completed actions. Мы решаем проблему вместе emphasizes the process of solving (we are in the midst of solving), so we use the imperfective решаем. A perfective counterpart would be мы решим проблему вместе (“we will solve the problem together”), focusing on the completion.

Why is there no preposition before проблему?

In Russian, direct objects usually do not require a preposition; they’re simply put into the accusative case. Prepositions like о or для would change the meaning (for example, о проблеме means “about the problem,” not “solve the problem”).

What part of speech is вместе, and how does it function here?