Does a speedy trial take 90 days?

A "speedy trial" has very little to do with the duration of a criminal proceeding in the presence of a judge and jury. It refers to the timeliness of the State's disposition of the criminal matter after it has identified an Accused and asserted its power over the Accused.

It is easer to understand by example: the State's prosecution arm, the District Attorney, obtains an indictment; the Accused is arraigned, that is, he goes before the Court to be formally informed of the criminal charges, and the if Accused promptly goes into the adjudication process: a crinimal trial before a judge and jury, and he is subjected to the risk of a determination that he has violated some law, it can be considered "speedy". On the other hand, if the District Attorney, or the State's prosecution arm, just does nothing, after a while, the unnecessary or protracted delay becomes a violation of the rights of a person to just get on with life without the risk of having it disrupted at any time at the whimsy of the State.

More or less, a speedy trial refers not so much to how long it takes in the courtroom but how long the process takes getting to the court room without life disrupting delays at the whimsy of the State.

Historically, the concept arrises from American colonists' experience with the Star Chamber; no longer in existence in England, the Star Chamber a prosecution arm of the government, could arrest a person, put them in chains, ship them back to England, never bother to let them know what they were accused of, and when the Star Chamber got around to it, have a more or less trial.

In the broadest sense, the concept of the speedy trial is a limitation restricting the government from the arbitrary exercise of power over the person.