LAWRENCE, Kan. — Kansas has struggled for years to find just one quarterback who could effectively run its offense.

Now, it appears the Jayhawks have two.

Montell Cozart and Ryan Willis seamlessly shared repetitions with the first team in a 55-6 rout of Rhode Island on Saturday , which ended the Jayhawks’ 15-game losing streak and gave second-year coach David Beaty his first victory. Cozart and Willis combined to throw for 343 yards and five touchdowns while sending Kansas to its highest point total in nearly a decade.

“What that did was just solidified what we saw throughout camp,” Beaty said. “I think I said it publicly quite a few times, both of those guys can play well in our system.”

The race for the starting job was close throughout the fall, and Beaty said he only decided on Cozart in the hours leading up to kickoff. But ultimately the title mattered little as both were given ample opportunities to lead the Jayhawks.

The quarterback duel wound up producing dual QBs. The way Kansas went about its substitutions on Saturday was prudent, too.

Rather than flip-flopping every series, each went two or three series a time, allowing them to get into rhythm. And while it turned out to be easy to do against an FCS bottom-dweller like Rhode Island, it still bred confidence in Cozart and Willis.

“Coach Beaty and the staff let us know we were going to be doing that,” Cozart said. “We’re for one another. We’re all for wins. At the end of the day, that’s what it’s all about.”

There’s an old adage that if you have two quarterbacks, you don’t have any, the idea being that it is better to have one clear-cut starter. But in Cozart and Willis, the Jayhawks have two QBs with enough difference in their skillsets that they just might coexist all season.

Cozart is more mobile than Willis, which allows the Jayhawks to use more exotic quarterback run schemes. Willis is a pure pocket passer more adept at running screens and quick hits. One thing is certain: Neither quarterback is fessing up to a bruised ego over splitting time.

“We’re for each other. We have five guys in the room who can do it,” Willis said, lumping Deondre Ford, Keaton Perry and freshman Carter Stanley in the mix. “I’ve said it over and over.”

One thing that is helping both quarterbacks is the improved personnel at their disposal.

Running back Ke’aun Kinner picked up where he left off last season, averaging nearly 10 yards per carry against Rhode Island. But sophomore Taylor Martin, transfer Denzell Evans and freshman Khalil Herbert also got onto the field, allowing the Jayhawks to better rotate fresh bodies.

In the passing game, LaQuvionte Gonzalez had seven catches for 78 yards and a touchdown in his first game with the Jayhawks. The transfer from Texas A&M had to sit out last season under the NCAA’s transfer guidelines, which meant he hadn’t played a game in nearly two years.

He was just one of five different receivers to catch a touchdown pass, the first time the Jayhawks have had that many players reach the end zone since a game against Central Michigan in 2007.

Kansas only completed 11 TD passes all of last season.

“You can just plug anyone in at any point and feel completely comfortable that they’re going to get the job done,” said sophomore Tyler Patrick, who hauled in one of the TD catches. “Everyone is just making everyone better and competing every day and that’s a really good thing.”

Rhode Island was overmatched, so it’s hard to put much stock into the Jayhawks’ season-opening performance. A better test comes this Saturday against Frank Solich and Ohio.

Still, their debut Saturday at least provided more reason to be optimistic about the season. Especially when it comes to who is under center.

“Both of them performed at a very high level,” Beaty said. “We have to take it one game at a time, and until someone completely separates themselves, we’ll continue to rotate quarterbacks. I know this: The majority of teams in the Big 12 last year needed a second quarterback.”