This is a subjective question—based on one's personal opinion. To me, it would seem that there are only two possible outcomes. The conflict will either continue or be resolved if the relationship between the girls changes for some reason.
In Toni Cade Bambara's "Raymond's Run," there are a couple of reasons at the start of the story to believe that nothing will change between Squeaky and Gretchen. First, Gretchen is relatively new to the neighborhood and the reader discovers that at least one of Squeaky's friends has left to hang out with Gretchen instead.
There is also a sense of competition between the two girls because Gretchen is also a runner. The enmity between the two girls is supported by what Squeaky sees as Mr. Pearson's ridiculous suggestion:
"That new girl should give you a run for your money." He looks around the park for Gretchen... "Wouldn't it be a nice gesture if you were...to ahhh..."
I give him such a look he couldn't finish putting that idea into words. Grownups have a lot of nerve sometimes... [I] stomp away, I'm so burnt.
However, the very competition that exists between them brings something new to Squeaky's mind, foreshadowing a change between them even before the race begins:
...I see Gretchen standing at the starting line, kicking her legs out like a pro.
Running is one of the most important things in the world to Squeaky, and she notices that Gretchen, in preparing for the race, also knows what she is doing.
The next observation clarifies more clearly what the end of the story might hold with regard to the conflict that exists with these girls:
...here comes Gretchen walking back...huffing and puffing with her hands on her hips taking it slow, breathing in steady time like a real pro and I sort of like her a little for the first time.
Because the reader knows how central running is to Squeaky and to her sense of accomplishment that validates her sense of self-worth, the one thing that would impress her more than anything is to see someone else with the same dedication to running and the skill to excel at the sport. After all, it is this realization that draws her attention to Raymond, seeing him in a new light after she watches him run.
With Squeaky's reflections in mind, we can postulate—immediately after the race—that what the girls have in common will overshadow the differences between them, and the conflict will be resolved.