Learn Italian: Come hai spiegato che saresti arrivato in ritardo? - How did you explain that you would arrive late?

In Italian, when you are talking about the past ("How did you explain") and refer to an action that was going to happen later ("that you would arrive"), you must use the past conditional. This is called the "future in the past." While English often uses the present conditional ("would arrive"), Italian strictly requires the past conditional (saresti arrivato).

Why is the auxiliary verb saresti used instead of avresti?

The past conditional is formed just like the passato prossimo, using an auxiliary verb (essere or avere) plus the past participle. Because arrivare (to arrive) is a verb of motion, it requires essere. Therefore, you use the conditional form of essere (saresti) rather than avere.

If I am female, do I need to change the ending of arrivato?

Yes! Because this compound tense uses the auxiliary verb essere, the past participle must agree with the subject in gender and number. If a woman is the one who was going to arrive late, the sentence becomes: Come hai spiegato che saresti arrivata in ritardo?

Could I say saresti arrivato tardi instead of in ritardo?

They have slightly different meanings. In ritardo specifically means "delayed" or "behind schedule" (like showing up late for a meeting or missing a scheduled arrival). Tardi generally means "late in the day" or "late at night". Since this sentence is about missing an expected arrival time, in ritardo is the most natural choice.