What happens to the calculation of speedy trial when a mistrial is declared

There is really no cut and dry answer to the situation you pose. While the U.S. Constitution guarantees a speedy and public trial, Washington court rules require (at least ostensibly) that an out of custody defendant be brought to trial within 90 days of arraignment, and those being held in jail should have a trial within 60 days. Like most court rules, however, the exceptions have grown like a weed, and have almost eclipsed the general rule. The court rules recognize periods of time during which these time frames "toll," or for lack of a better word, "don't count." In the situation you describe, your brother will probably have a new trial set, the court finding reason to toll the period of speedy trial. While this doesn't seem fair, realize that Washington's 90 day rule is rather more liberal than those in many other states.