The smile that Squeaky and Gretchen give each other is a smile of mutual respect and hard work. It is a smile of appreciation between two competitors. You see the same thing in all kinds of sports. When a baseball player gets a great base hit, it's fairly common to see the first baseman and the runner have a friendly exchange as the next batter comes to the plate. They are on opposite teams and competing against each other, but that doesn't mean the players don't recognize the talent of opponents.
Squeaky does the same thing with Gretchen. Up until the end of the story, Squeaky is entirely focused on herself, her running, and how much better she is at it than everybody else.
“I always win cause I’m the best,” I say straight at Gretchen who is, as far as I’m concerned, the only one talking in this ventrilo-quist-dummy routine.
When Squeaky first tells the reader about Gretchen, it's clear that Squeaky has very little respect for her. Squeaky doesn't believe that Gretchen knows a thing about running; therefore, she should be easy to beat. But as the girls get on the starting line, Squeaky is forced to begin reconsidering her initial observations about Gretchen.
I get up and slip off my sweat pants and then I see Gretchen standing at the starting line, kicking her legs out like a pro.
Squeaky does win the race, but only just ahead of Gretchen. Moments after the race, Squeaky sees Gretchen again acting like a pro runner.
And I lean down to catch my breath and here comes Gretchen walking back, for she’s overshot the finish line too, 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.
It actually takes a few minutes for the judges to decide who actually won the race. It was that close. During that time, Squeaky is forced to consider Gretchen as an equal. Someone who loves running as much as she does. Someone who works hard at it like she does. Squeaky eventually decides that it doesn't matter who won or lost that race. She now has a kinship with Gretchen that only runners and fellow competitors understand and respect about each other. That's why they smile.
And I look over at Gretchen wondering what the “P” stands for. And I smile. Cause she’s good, no doubt about it. Maybe she’d like to help me coach Raymond; she obviously is serious about running, as any fool can see. And she nods to congratulate me and then she smiles. And I smile. We stand there with this big smile of respect between us.
At the end of the story Squeaky and Gretchen smile at each other as a sign of mutual respect. Both girls recognize in each other an opponent worthy of respect. Squeaky realizes that Gretchen is just as serious about running as she is and appreciates this. It also shows the awakening and growth of Squeaky as a character; up to this point in the story she remains unchanged (flat character).
Squeaky and Gretchen smile at each other at the end of the race because by now they both respect each other. Also Squeaky realizes that Gretchen also tries her best at running and is just as serious.