Mi hermana salió agotada del trabajo, pero aun así fue al gimnasio.

Salió is the preterite form of salir for ella: she left / went out.

In this sentence, it refers to a completed action in the past: she left work, and then she went to the gym. Spanish often uses the preterite for this kind of finished event in a sequence.

So:

• salió del trabajo = she left work
• fue al gimnasio = she went to the gym

Using the preterite in both verbs helps show a clear chain of completed actions.

Because agotada describes mi hermana, and hermana is feminine singular.

Adjectives in Spanish usually agree with the noun they describe:

• agotado = masculine singular
• agotada = feminine singular
• agotados = masculine plural
• agotadas = feminine plural

Since the person is my sister, the adjective must be agotada.

This is a very common Spanish pattern: verb + adjective to describe the state someone was in when the action happened or the resulting state.

So salió agotada del trabajo means she left work exhausted.

The adjective agotada is not replacing the verb. Instead, it adds information about how she was when she left.

Similar examples:

• Llegó cansado = He arrived tired.
• Volvió contenta = She came back happy.
• Salieron enfadados = They left angry.

Because de + el contracts to del in Spanish.

So:

• de el trabajo → del trabajo

This contraction is mandatory, except when el is part of a proper name, such as El Escorial.

You also see the same kind of contraction with:

• a + el → al

That is why the sentence also has al gimnasio.

Fue is preterite, and iba is imperfect.

Here, fue al gimnasio is used because the sentence is talking about one completed action in a specific situation: despite being exhausted, she did go to the gym.

Compare:

• Fue al gimnasio = She went to the gym.
  Completed event.

• Iba al gimnasio = She was going to the gym / used to go to the gym.
  Ongoing action, background, or habit.

In this sentence, the speaker is telling a specific past event, so fue fits better.

Aun así means something like even so, all the same, or nevertheless.

It shows contrast:

• She was exhausted.
• Even so, she went to the gym.

It is similar to expressions like:

• sin embargo
• a pesar de eso
• con todo

But aun así is very natural and common in this type of sentence.

Here, aun is normally written without an accent because it means something like even or even so.

A useful rule is:

• aún with an accent usually means still / yet
• aun without an accent often means even / including / despite that

So in aun así, the meaning is closer to even so, not still so, which is why aun is usually written without the accent.

Spanish often drops subject pronouns when the verb form already makes the subject clear.

Here:

• salió
• fue

Both forms can refer to he/she/you (formal), but since the sentence already says Mi hermana, there is no need to add ella.

So Spanish prefers:

• Mi hermana salió agotada...

rather than:

• Mi hermana ella salió agotada...

Adding ella would usually sound unnecessary unless you want emphasis or contrast.

Because Spanish can drop subjects, but it does not have to. Speakers often include the subject noun when they want to:

• introduce who they are talking about
• make the sentence clearer
• create contrast with another person
• give the sentence a natural starting point

So Mi hermana is there because the speaker wants to identify the subject explicitly. After that, Spanish does not need ella as well.

Using both pero and aun así strengthens the contrast.

• pero = but
• aun así = even so / nevertheless

Together, they create a very natural structure in Spanish:

• ..., pero aun así ...

It sounds like:

• ..., but even so ...

You could remove one of them, but the sentence would feel slightly different:

• Mi hermana salió agotada del trabajo, pero fue al gimnasio.
• Mi hermana salió agotada del trabajo; aun así, fue al gimnasio.

All are correct, but the original version is especially expressive.

Yes. Aun así is fairly flexible.

These are all possible:

• Mi hermana salió agotada del trabajo, pero aun así fue al gimnasio.
• Mi hermana salió agotada del trabajo; aun así, fue al gimnasio.
• Mi hermana salió agotada del trabajo, pero fue al gimnasio aun así.

The original version is very natural because aun así comes right before the second verb and highlights the contrast clearly.

It is a very common expression. Salir del trabajo means to leave work.

It can refer to:

• physically leaving the workplace
• finishing work and going out

So salió del trabajo is a very normal way to say she got out of work / she left work.

Similar expressions:

• salir de casa = leave home
• salir de la oficina = leave the office
• salir de clase = leave class

Because the sentence tells a completed past sequence:

1. She left work exhausted.
2. Even so, she went to the gym.

The preterite is especially common when Spanish narrates events one after another. It gives the sense of a finished story line.

If the imperfect were used instead, the meaning would shift toward background, habit, or ongoing action, which is not the main idea here.