In the 13 seconds it took a police officer to respond, a homeless woman believed to be mentally ill allegedly plunged a butcher knife again and again into two tourists, killing them on a busy Atlantic City street.

The officer was part of the beefed-up security in the tourism area, but the show of force wasn't enough to save the women — and it won't be enough to save Atlantic City, so long as its decades-old and overwhelming homelessness problem continues to go untreated.

The system is broken. Three days after the killings, police and human-service workers found a mentally ill woman sleeping under the boardwalk. She attacked them. They took her to a hospital. Less than an hour later, the hospital put her back on the streets, saying she was too violent.

This is a routine event in a town where a quarter of the state's 12,000 unemployed, underemployed, drug-addicted, and mentally and physically ill homeless end up at the almost 50-year-old Atlantic City Rescue Mission, which tries to channel them into treatment or jobs. Another thousand spend nights under the boardwalk, also known as the "Underwood Hotel," or in halfway houses and abandoned buildings.

Why not come to A.C.? With all the casinos, the panhandling and mugging opportunities are plentiful enough to feed a drug or alcohol problem, or to just get through a hard time. There's a methadone clinic whose neighborhood is dubbed "Zombieland," a soup kitchen, and social services — all within walking distance.

Some homeless come on their own. Others were given one-way bus tickets by social-service agencies, hospitals, or police in towns that can't, or won't, deal with them.

The closest other shelters are in Mercer and Cumberland Counties, but Bill Southrey, head of the Atlantic City mission, says his is the only one in the region that takes people even if they don't have disability or other benefits.

That makes Atlantic City's homelessness a regional problem, ripe for state intervention.

Gov. Christie has created a tourism district, with control of policing and sanitation. Ambassadors direct tourists to attractions and report problems. That is a good start, but it's not the comprehensive approach that's needed.

No decent society can allow people to suffer the way the homeless do, with untreated mental and physical problems. But if compassion isn't enough motivation, Christie should see last week's killings as a sign written with neon lights that say either properly deal with the homeless or see the idea of Atlantic City as a resort hit the skids.