Мы бежали быстро, но так и не смогли догнать троллейбус.

Yes, Russian often omits subject pronouns when the verb already makes the subject clear. Since бежали and смогли are both we forms, the sentence could be shortened to:

Бежали быстро, но так и не смогли догнать троллейбус.

Including мы makes the subject more explicit. It can add clarity, contrast, or simply sound more natural in context. So мы is not required, but it is perfectly normal.

Бежали is the past tense, plural form of бежать = to run.

Breakdown:

• бежать = to run
• бежал = he ran / was running
• бежала = she ran / was running
• бежало = it ran / was running
• бежали = they ran / we ran / you all ran

Because the subject is мы, Russian uses the plural past form бежали.

Also, бежать is an imperfective verb, so here it focuses on the process: we were running / we ran.

Быстро is an adverb, meaning quickly / fast. Adverbs in Russian usually do not change for gender, number, or case.

It modifies the verb бежали, so:

• бежали быстро = ran quickly / were running fast

Compare:

• быстрый = fast (masculine adjective)
• быстрая = fast (feminine adjective)
• быстро = quickly / fast (adverb)

So here you need the adverb, not the adjective.

Так и не is a very common Russian expression. It adds the idea of despite everything, in the end not, or never did manage to.

So:

• не смогли догнать = did not manage to catch up
• так и не смогли догнать = still didn’t manage to catch up, never did manage to catch up

It often suggests:

• there was an effort
• the result was expected or hoped for
• but the result never happened

So the sentence has a stronger feeling than just a plain negative. It emphasizes failure after trying.

Смогли is the past plural of смочь, the perfective partner of мочь.

• мочь = to be able, can
• смочь = to manage to, succeed in being able to

In this sentence, the speaker is talking about a completed result: whether they succeeded or not. Since they are talking about the outcome, Russian prefers the perfective verb:

• не смогли догнать = did not manage to catch up

If you used могли, it would usually sound more like were able / could, referring more to ability in general, not the final outcome.

So смогли is the natural choice when talking about whether the attempt succeeded.

Догнать is a perfective verb meaning to catch up with or to overtake by reaching. It focuses on the result: actually reaching the trolleybus.

Догонять is the imperfective partner, which focuses more on the process of catching up.

Compare:

• догонять троллейбус = to be catching up to the trolleybus / to try to catch up
• догнать троллейбус = to catch up to the trolleybus successfully

Since the sentence says they did not manage to achieve that result, Russian uses the perfective infinitive:

• не смогли догнать = did not manage to catch up

This is very common: after смочь, Russian often uses a perfective infinitive when the focus is on achieving a result.

Троллейбус is in the accusative case, because it is the direct object of догнать.

You are catching up to what?

• троллейбус

For many masculine inanimate nouns, the accusative singular looks exactly the same as the nominative singular.

So:

• nominative: троллейбус
• accusative: троллейбус

That is why the form does not change.

Compare with a feminine noun:

• машина → машину

And compare with an animate masculine noun:

• брат → брата

Но means but and is the natural choice here because the second clause contrasts sharply with the first:

• Мы бежали быстро = we ran fast
• но так и не смогли догнать троллейбус = but still didn’t manage to catch up to the trolleybus

This is a strong contrast between effort and failure.

А can also connect contrasting ideas, but it often feels softer or more like whereas / while / and yet, depending on context. In this sentence, но is more natural because the contradiction is stronger:

• they ran fast
• but the expected result still did not happen

Yes, Russian word order is flexible, although different orders can change the emphasis.

The neutral order here is:

• Мы бежали быстро, но так и не смогли догнать троллейбус.

Other possible versions:

• Мы быстро бежали, но так и не смогли догнать троллейбус.
• Троллейбус мы так и не смогли догнать, хотя бежали быстро.

These are all grammatical, but they emphasize different parts.

In the original sentence:

• first comes the action: we ran quickly
• then the disappointing result: but still didn’t catch up

That order sounds natural and clear.

It can mean either, depending on context.

Because бежать is imperfective, бежали can describe:

• an ongoing action in the past: were running
• a simple past action without focusing on completion: ran

In this sentence, English could translate it as either:

• We were running fast, but still couldn’t catch up to the trolleybus.
• We ran fast, but still couldn’t catch up to the trolleybus.

The Russian sentence itself does not force only one of those English options. The context would decide which is best.

Yes. The sentence suggests effort that failed to produce the expected result.

The key parts that create this feeling are:

• бежали быстро = they made a real effort
• но = strong contrast
• так и не = despite that effort, the result never happened
• не смогли догнать = they failed to achieve the goal

So the overall tone is something like:

• We ran fast, but still never managed to catch up to the trolleybus.

It sounds slightly more expressive than a plain factual statement, because it highlights frustration or disappointment.