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.
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:
So tragar adds a sense of haste and perhaps a slightly rougher, more vivid tone.
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:
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:
In Spain, deprisa is very common in speech.
You may also hear:
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.
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:
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.
This is different from:
For this sentence, porque is correct because it gives the cause of the action.
Yes. Spanish adverbs often have some flexibility.
The original:
Also possible:
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:
A native speaker might also say similar versions such as: