Við biðum í þrjátíu mínútur í þvottahúsinu af því að þvottavélin stoppaði.

Biðum is the 1st person plural past tense of bíða (to wait).

So:

• að bíða = to wait
• við bíðum = we wait / we are waiting (present)
• við biðum = we waited / we were waiting (past)

A common thing that surprises learners is that the present and past plural forms look very similar here. The difference is the accent:

• bíðum = present
• biðum = past

So in this sentence, Við biðum means we waited or we were waiting, depending on context.

It can mean either, depending on context.

Icelandic does not use a tense system exactly like English. Very often, the simple past can cover both:

• we waited
• we were waiting

So Við biðum can be understood as either a completed past action or an ongoing past situation. English usually forces you to choose more clearly than Icelandic does.

That is very common in Icelandic. The preposition í can mean different things depending on context.

Here it appears in two different uses:

1. í þrjátíu mínútur = for thirty minutes
   Here, í is used in a time expression showing duration.

2. í þvottahúsinu = in the laundry room
   Here, í shows location.

So even though both are í, they are doing different jobs:

• time span: í þrjátíu mínútur
• place/location: í þvottahúsinu

In Icelandic, í + accusative is often used to express how long something lasts.

So:

• í eina klukkustund = for one hour
• í tvo daga = for two days
• í þrjátíu mínútur = for thirty minutes

This is a very common pattern, and it does not mean movement here. It is simply a set time-expression structure.

Also, mínútur is plural because thirty minutes is plural.

Because this phrase describes being in a place, not moving into it.

With í, Icelandic often makes a case distinction:

• accusative for motion into
• dative for location in

So compare:

• Ég fór í húsið = I went into the house
• Ég var í húsinu = I was in the house

In your sentence, the people were waiting in the laundry room, so this is location, which is why Icelandic uses the dative form:

• í þvottahúsinu

Þvottahúsinu is the dative singular definite form of þvottahús (laundry room / wash house).

Breakdown:

• þvottahús = laundry room
• þvottahúsi = in/to the laundry room depending on context and case pattern
• þvottahúsinu = the laundry room in the dative singular definite

The ending -inu here shows that the noun is:

• definite = the
• singular
• dative
• and the noun itself is neuter

That is why Icelandic says þvottahúsinu instead of using a separate word for the.

Because Icelandic usually expresses the definite article as a suffix, not as a separate word like English the.

So:

• þvottavél = washing machine
• þvottavélin = the washing machine

And:

• þvottahús = laundry room
• þvottahúsinu = in the laundry room / the laundry room in dative

The exact form of that attached article changes depending on:

• gender
• number
• case

So the endings are not the same on every noun.

Because the two nouns have different genders and different cases.

• þvottavél is feminine
• þvottahús is neuter

Also, in this sentence:

• þvottavélin is the subject, so it is in the nominative
• þvottahúsinu comes after í in a location phrase, so it is in the dative

So the endings are different because Icelandic nouns change form based on grammar.

A rough comparison:

• þvottavélin = nominative singular definite feminine
• þvottahúsinu = dative singular definite neuter

Yes. Af því að is a very common fixed expression meaning because.

In this sentence:

• af því að þvottavélin stoppaði = because the washing machine stopped

Learners sometimes try to analyze it word by word, and historically it does come from smaller parts, but in normal modern Icelandic it is best learned as a set conjunction meaning because.

Other ways to say because exist too, such as:

• því að
• vegna þess að

But af því að is extremely common and natural.

Because after af því að, you get a subordinate clause, and subordinate clauses in Icelandic usually do not follow the normal main-clause verb-second pattern.

So:

• Main clause: Við biðum ...
• Subordinate clause: af því að þvottavélin stoppaði

Inside that subordinate clause, the normal order is:

• subject + verb
• þvottavélin stoppaði

That is why you do not get af því að stoppaði þvottavélin here.

Because its subject, þvottavélin (the washing machine), is singular.

So the verb agrees with that subject:

• þvottavélin stoppaði = the washing machine stopped

If the subject were plural, the verb form would change accordingly.

Also, stoppaði is the past tense of stoppa (to stop), and it is a very straightforward weak-verb past form.

Icelandic makes a lot of compound nouns, and these are very useful to learn.

Here:

• þvottahús = laundry room
• þvottavél = washing machine

They are built from þvott-, which relates to washing / laundry, plus another noun:

• hús = house / building / room
• vél = machine

So:

• þvottahús = literally something like wash-house / laundry room
• þvottavél = literally washing machine

Getting comfortable with compounds is a big part of learning Icelandic vocabulary.

These two letters are often new for English speakers:

• þ is like the th in thin
• ð is like the th in this

Examples from the sentence:

• þrjátíu
• þvottahúsinu
• af því að

A small extra note: ð can sometimes sound weaker than English speakers expect, especially in everyday speech. In a word like við, the final ð may be very soft.

So even if you do not pronounce every ð very strongly at first, that is normal.