Hvis strygejernet havde virket, ville min søster have været færdig tidligere.

This is a past unreal conditional: something did not happen in the past, and the sentence describes the imagined result.

The pattern is:

Hvis + past perfect, ville + have + past participle

So here:

• Hvis strygejernet havde virket = the unreal past condition
• ville min søster have været færdig tidligere = the imagined past result

It is very close to the English If the iron had worked, my sister would have finished earlier / would have been finished earlier.

Havde virket is the past perfect.

It is formed with:

• havde = had
• virket = worked / functioned

In Danish, the past unreal if-clause normally uses the past perfect to show that the condition belongs to an earlier past situation that did not happen.

So:

• virkede = worked / was working
• havde virket = had worked

In this sentence, havde virket tells you: the iron did not actually work, but we are imagining that it had.

Because in ordinary conditionals, Danish normally does not use ville after hvis.

So the natural pattern is:

• Hvis strygejernet havde virket ... not
• Hvis strygejernet ville have virket ...

This is similar to standard English, where we usually say:

• If it had worked ... not
• If it would have worked ...

So ville belongs in the main clause here, not in the hvis-clause.

This is the conditional perfect in the main clause. It shows the imagined result in the past.

It is built like this:

• ville
• have
• været

Together, ville have været means would have been.

So the sentence is not about a present or future result. It is about a result that would already have been true in the past.

Compare:

• ville være færdig = would be finished
• ville have været færdig = would have been finished

Here, the second one is needed because the whole situation is in the past.

This is because Danish is a V2 language in main clauses. That means the finite verb normally comes in the second position.

The first position here is occupied by the whole if-clause:

Hvis strygejernet havde virket

After that, the main clause begins, and its finite verb must come next:

ville

So the order becomes:

Hvis strygejernet havde virket, ville min søster have været færdig tidligere.

If the main clause came first, you would get:

Min søster ville have været færdig tidligere, hvis strygejernet havde virket.

Both are correct.

Because hvis introduces a subordinate clause, and subordinate clauses in Danish normally keep the more basic order:

subject + finite verb

So:

• Hvis strygejernet havde virket = correct
• Hvis havde strygejernet virket = not correct here

Inversion is typical of Danish main clauses, not ordinary hvis-clauses.

Strygejernet is the definite singular form of strygejern.

The noun is:

• et strygejern = an iron
• strygejernet = the iron

The ending -et is the definite article for many neuter nouns in Danish.

So instead of using a separate word for the, Danish often adds it to the end of the noun.

Because færdig agrees with the subject.

The subject is:

min søster

That is a common gender singular noun, so the predicate adjective is:

færdig

Compare:

• min søster er færdig = my sister is finished / ready
• barnet er færdigt = the child is finished / ready
• de er færdige = they are finished / ready

So in your sentence, færdig is correct because it matches min søster.

Tidligere means earlier.

In this sentence, it means that your sister would have been finished earlier than she actually was.

Tidligere is very natural when you want to express earlier in time without adding another full comparison.

Før often means before, and it frequently connects to something else:

• før klokken fem = before five o’clock
• før jeg kom hjem = before I came home

At the end of this sentence, tidligere is the most natural choice.

Yes. In this sentence, virke means to work / function.

So strygejernet havde virket means the iron had been functioning properly.

A close alternative would be fungere:

• Hvis strygejernet havde fungeret ...

That would also be understandable, but virke is very natural Danish here.

Yes, in standard Danish writing, a subordinate clause like the hvis-clause is separated from the main clause with a comma.

So:

Hvis strygejernet havde virket, ville min søster have været færdig tidligere.

That comma helps mark the boundary between:

• the condition
• the result

It is standard and expected in normal written Danish.