Tuve que tragar el último bocado deprisa porque llegaba tarde.

Tuve que + infinitive means I had to + verb.

• tuve = the yo form of tener in the preterite
• que = to
• tragar = to swallow / gulp down

So:

• Tuve que tragar = I had to swallow / gulp down

This is a very common Spanish structure:

• Tuve que salir = I had to leave
• Tuvimos que esperar = We had to wait

Because tuve que usually refers to a specific completed obligation in the past.

In this sentence, the speaker is talking about one particular moment: they had to quickly swallow the last bite because they were running late.

• Tuve que... = I had to... (on that occasion, as a completed event)
• Tenía que... = I had to / was supposed to... (more ongoing, habitual, or background)

Compare:

• Tuve que salir corriendo.
  = I had to run out / I ended up having to leave quickly.

• Tenía que salir a las ocho.
  = I had to leave at eight / I was supposed to leave at eight.

So tuve que fits the idea of a single, completed situation.

Tragar literally means to swallow, and in many contexts it can suggest swallowing quickly, almost without properly chewing or enjoying the food.

That is why it works well here: the speaker was late, so they did not calmly eat the last bite; they kind of gulped it down.

Compare:

• comer el último bocado = eat the last bite
• tragar el último bocado = swallow/gulp down the last bite

So tragar adds a sense of haste and perhaps a slightly rougher, more vivid tone.

Bocado means bite or mouthful.

In el último bocado, it means the last bite of the food.

Examples:

• Dame un bocado. = Give me a bite.
• Me queda un último bocado. = I have one last bite left.

It is a very natural word when talking about food in small portions taken into the mouth.

Spanish often uses the definite article el / la / los / las in places where English may or may not use the.

Here, el último bocado is the natural way to say the last bite.

Without the article, último bocado, the phrase would usually sound incomplete in a normal sentence.

So:

• el último bocado = the last bite

This is just the standard, idiomatic form.

Deprisa means quickly / in a hurry / fast.

Yes, rápidamente is possible, but deprisa often sounds more natural and conversational in everyday speech, especially in Spain.

Compare:

• tragar el último bocado deprisa = swallow the last bite quickly / in a hurry
• tragar el último bocado rápidamente = also correct, but a bit more neutral or formal-sounding

In Spain, deprisa is very common in speech.

You may also hear:

• rápido used adverbially in informal speech
• con prisa = in a hurry

Because llegaba tarde here describes an ongoing situation or background state: the person was running late.

It does not mean they actually arrived late at that moment.
It means that, at the time of swallowing the last bite, they were already behind schedule.

• llegaba tarde = I was running late / I was going to be late
• llegué tarde = I arrived late

So the sentence is not focused on the final arrival. It is focused on the reason for the hurried action.

That is why the imperfect works well here: it gives background information.

Literally, it comes from llegar tarde, which is to arrive late, but in real usage Spanish often uses it to mean to be running late.

So in this sentence, a natural English interpretation is:

• porque llegaba tarde = because I was running late

This is very common in Spanish. It does not necessarily mean the arrival had already happened.

Because porque as one word means because and introduces the reason.

• porque llegaba tarde = because I was running late

This is different from:

• por qué = why
• el porqué = the reason / the why
• por que = a less common combination in other structures

For this sentence, porque is correct because it gives the cause of the action.

Yes. Spanish adverbs often have some flexibility.

The original:

• Tuve que tragar el último bocado deprisa porque llegaba tarde.

Also possible:

• Tuve que tragar deprisa el último bocado porque llegaba tarde.

But the original sounds very natural. Placing deprisa after el último bocado works well and keeps the sentence flowing smoothly.

In everyday Spanish, word order can shift a bit for rhythm or emphasis, but not every option sounds equally natural. The given version is a good standard choice.

Yes, it sounds natural in Spain.

A few points that make it feel natural:

• tuve que is a very common way to express a specific past obligation
• tragar gives a vivid idea of swallowing/gulping something down quickly
• bocado is a normal word for bite
• deprisa is especially common in Spain
• llegaba tarde is a natural way to say was running late

A native speaker might also say similar versions such as:

• Tuve que comerme el último bocado deprisa porque llegaba tarde.
• Me tuve que tragar el último bocado deprisa porque llegaba tarde.

But the original sentence is already perfectly natural.