All 120 Brockton firefighters have been trained in the administration of Narcan, a drug that can reverse the effects of an opiate overdose, Mayor Bill Carpenter said. The effort, which came together over the past few weeks, is part of an emergency effort to quell a surge in overdoses, he said in an interview Wednesday. “There have been six deaths in Brockton in the last 10 days from overdoses,’’ Carpenter said. “I don’t want anyone dying in my city. I’m trying to be proactive.” As first responders, Carpenter said, city firefighters can arrive at a scene as much as eight minutes before an ambulance, and there is no time to waste. Treating overdoses is just a symptom of the problem, however, the mayor said. “First we have to save peoples’ lives, then help them treat addiction,” he said.