Within a few years, times were dropping all over the nation.

But then a debate arose.

A paper by Dr. Peterson, the Duke cardiologist, and his colleagues, published in The New England Journal of Medicine in 2013, said that even though times had plummeted, the death rates for heart attack patients whose arteries were opened with balloons and stents had not budged. Could it be that faster just seemed better but that it actually made no difference to patient outcomes?

“That was demoralizing,” Dr. Krumholz said. But he did an analysis that found that the universe of heart attack patients being treated with stents and balloons had changed markedly. It used to be just the younger and healthier people who were more likely to have their arteries opened. Now, as the procedure became more popular and so many more people were treated this way, the group included more older and sicker people.

Dr. Peterson concluded that analyses like his and Dr. Krumholz’s had challenges. The problem, he said, is that it is hard to accurately compare treatments given at different points. Nonetheless, the consensus — which he shares with Dr. Krumholz and other leading cardiologists — is that the shorter times and improved medical care contributed to the declining death rates and better outcomes for heart attack patients.

A Never-Ending Mission

At Lourdes, the push to be faster — and to fix the problems that slow things down — continues.

The weekend that Ms. Samuels was rushed to Lourdes, two other heart attack patients were brought in. First was Kevin Whisler, 43, a postal worker by day and forklift operator by night. He had been having what he thought was heartburn for two days, gulping Tums, Rolaids and Pepcid. Finally, on Saturday night, March 28, he went to an urgent care center, where a practitioner did an electrocardiogram and called an ambulance.

“You’ve got to be kidding me,” Mr. Whisler said. “I go in for heartburn and now you tell me I’m having a heart attack?”

Mr. Whisler’s doctor had prescribed a statin for his high cholesterol level and a medication for his diabetes. But Mr. Whisler said he thought he was too young to be taking pills every day and was trying to control his risk factors with diet.