Automaten er ny nok til at virke hurtigt, men billetautomaten er for langsom i dag.

In Danish, the definite article is usually added to the end of the noun, not placed in front of it as a separate word like English the.

• automat = machine / vending machine
• automaten = the machine

And:

• billetautomat = ticket machine
• billetautomaten = the ticket machine

This is very common in Danish:

• en bil → bilen
• en bog → bogen
• en automat → automaten

So the -en ending here means the.

Billetautomaten is a more specific noun. It is a compound noun:

• billet = ticket
• automat = machine
• billetautomat = ticket machine

So:

• automaten = the machine
• billetautomaten = the ticket machine

A learner may wonder why both are used in the same sentence. Danish often uses a general noun first and then a more specific one later. Depending on context, they may or may not refer to the same machine. Grammatically, both are perfectly normal.

Because Danish, like German, very often forms compound nouns as one single word.

So instead of writing:

• billet automat

Danish writes:

• billetautomat

This is the standard way to make compounds:

• togstation = train station
• busbillet = bus ticket
• billetautomat = ticket machine

When the noun becomes definite, the definite ending is added to the whole compound:

• billetautomat → billetautomaten

Nok means enough here, and til at introduces the infinitive phrase that follows.

So the pattern is:

• adjective + nok til at + infinitive

In this sentence:

• ny nok til at virke hurtigt
  = new enough to work quickly

More examples:

• gammel nok til at stemme = old enough to vote
• stærk nok til at løfte den = strong enough to lift it

So nok is not just a general filler word here. It specifically means enough.

Because in Danish, nok normally comes after the adjective when it means enough.

So:

• ny nok = new enough
• hurtig nok = fast enough
• stor nok = big enough

This is different from English, where enough also comes after the adjective:

• new enough
• fast enough

So this part is actually quite similar in the two languages.

Because hurtigt is being used as an adverb, meaning quickly.

• hurtig = quick / fast (adjective)
• hurtigt = quickly / fast (adverb)

In Danish, adverbs are often formed using the -t form of the adjective.

So:

• en hurtig maskine = a fast machine
• maskinen virker hurtigt = the machine works quickly

In your sentence, hurtigt describes how it works, not what the machine itself is like. That is why the adverb form is used.

Here virke means something like to work, to function, or to operate.

So:

• virke hurtigt = work quickly / function quickly

Be careful, because virke can have several meanings in Danish depending on context, including:

• to work/function
• to seem/appear

For example:

• Maskinen virker ikke. = The machine doesn’t work.
• Han virker træt. = He seems tired.

In your sentence, the meaning is clearly function/work.

Here for means too, not the English preposition for.

So:

• for langsom = too slow
• for dyr = too expensive
• for stor = too big

This is a very common Danish use of for.

So the second part of the sentence:

• billetautomaten er for langsom i dag

means:

• the ticket machine is too slow today

Because men joins two full clauses, and each clause needs its own verb.

The sentence is:

1. Automaten er ny nok til at virke hurtigt
2. men billetautomaten er for langsom i dag

Each of those is a complete clause with its own subject and verb:

• Automaten
  • er
• billetautomaten
  • er

That is why the second er cannot be omitted.

I dag means today, and time expressions often come late in a Danish clause, especially after the main descriptive part.

So this is very natural:

• billetautomaten er for langsom i dag

But Danish word order is flexible, and i dag could also be moved to the front for emphasis:

• I dag er billetautomaten for langsom.

When a time expression comes first, the verb usually comes before the subject in the main clause:

• I dag er billetautomaten ...

This is normal Danish V2 word order.

Yes. A very natural alternative would be:

• I dag er billetautomaten for langsom.

Danish main clauses usually follow the verb-second rule, often called V2. That means the finite verb comes in second position.

So compare:

• Billetautomaten er for langsom i dag.
• I dag er billetautomaten for langsom.

Both are correct. The second version gives a little more emphasis to today.

Because Danish usually marks definiteness with an ending attached to the noun.

English says:

• the machine
• the ticket machine

Danish usually says:

• automaten
• billetautomaten

So instead of a separate the, Danish often uses:

• -en
• -et
• -ne

depending on the noun.

This is one of the biggest structural differences from English.

Yes, very much so. It is a common pattern:

• [adjective] + nok til at + [infinitive]

Examples:

• Han er gammel nok til at køre bil. = He is old enough to drive.
• Systemet er hurtigt nok til at klare opgaven. = The system is fast enough to handle the task.
• Automaten er ny nok til at virke hurtigt. = The machine is new enough to work quickly.

If you learn this as a chunk, it will be very useful.

Men means but, and it introduces a contrast.

The contrast here is:

• the machine is new enough to work quickly
  but
• the ticket machine is too slow today

So men is the natural conjunction because the second clause contrasts with the expectation created by the first. If something is new enough, you might expect it to work quickly, so men signals that the reality is different.

Formally, it is the -t form of the adjective hurtig, and that same form is often used as an adverb.

So in practice, learners usually think of it like this:

• hurtig = fast, quick
• hurtigt = quickly / fast

That is a useful way to understand it in this sentence.

So yes, historically and grammatically it is the -t form, but in this sentence it functions as an adverb, because it describes the verb virke.

Not in this sentence. Although virke can mean seem, the combination here clearly points to function/work quickly.

That is because:

• the subject is a machine
• the context is about speed and performance
• the second clause says it is too slow today

So the meaning is about operation, not appearance. A machine can virke hurtigt in the sense of operate quickly. Here, seem quick would not fit the context well.