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?

Вместе is an adverb meaning “together.” It modifies the verb phrase решаем проблему, indicating that the action is carried out jointly by the subject мы.

Can вместе go elsewhere in the sentence for emphasis?

Yes. Russian has relatively free word order. You could say Вместе мы решаем проблему, putting вместе first for emphasis (“Together, we are solving the problem”). The core grammatical relationships stay the same because of the case endings.

Why do we use мы explicitly here? Could it be dropped?

Technically you could drop мы, since решаем already indicates first-person plural (“we”). However, adding мы adds clarity or emphasis on who is doing the action. In spoken or casual Russian, subjects can be omitted if the meaning remains clear.

What is the stress pattern in решаем and проблему вместе?

In решаем the stress falls on the second syllable: re-SHÁ-em. In проблему it’s on the second syllable: pro-BLE-mu. In вместе the stress is on the first syllable: VMYEH-sʲe.

Could we switch to a more colloquial verb for “solve” here?

Yes, in informal contexts you might hear разбираем проблему вместе (“we’re working through/figuring out the problem together”). Разбираться has a slightly different nuance (“to sort out” or “to figure out”) but is common in speech.

Is there any nuance in using решаем versus разрешаем?

Yes. Решать means “to solve” or “to decide.” Разрешать (imperfective) means “to allow” or “to permit.” Despite the similar form, they are different verbs. The perfective of решать is решить, while for разрешать, the perfective is разрешить.

How would you say “We have solved the problem together” in Russian?

You’d use the perfective past form: Мы решили проблему вместе. Here решили is “solved” (perfective past), проблему remains accusative, and вместе stays as “together.”