Rinko is an anime-only character who challenged Ranma, albeit indirectly, in order to see who was the better driver and get the ¥10,000 along with full course dinner-for-two that was on offer as the prize for whoever won.
Due to the nature of her hobby/occupation (Kart racing), Rinko is very competitive about showing her skills as well as her title as the record holder of the circuit. Rinko is also rather short tempered as shown by how angry she becomes when multiple people overtake her during her race with Ranma and co. (which isn't real helped by having Shampoo insult her when she tries to pass Rinko.)
After Happosai ate the picnic the Tendos, Dr. Tofu, Ranma and Genma had planned to enjoy during there visit to the The Amusement Park. When Ranma learns about a race that's happening at the Amusement Park he decides to enter in order to win the not just the ¥10,000 but the full course dinner-for-two. Once Ranma has changed into his cursed form (as Dr. Tofu mentioned the karts seemed more suited for female drivers) and entered and is waiting to start she meets a woman with dark blue hair, wearing a green racing outfit. The woman then comments on how confident Ranma is, but then says that talk is cheap and they'll see who the better driver is when the race begins. She then puts on a pair of racing gloves and walks off. Ranma then learns from one of the Pit crew that the woman is called Rinko and is the current lap record holder.
Once the race begins Ranma and Rinko storm ahead into the top positions, with Rinko slightly in the lead. However, when Rinko sees Ranma coming up beside her she begins to accelerate even more while Ranma tries, and succeeds, to keep up with her. Despite Rinko's best attempts of keeping Ranma behind her, Ranma manages to sneak past and take the lead. This angers Rinko greatly so she shifts into overdrive and begins to ram into the back of Ranma's kart in an attempt to get past. However, just as Rinko is about to finish off Ranma, Happosai comes from behind Rinko, overtakes her, and begins to ask Ranma is she'd like to eat the full course dinner with him, an offer which Ranma declines quickly.
Being overtaken a second time angers Rinko even more, and she comments about being sick of getting overtaken. Just then Shampoo rams into the back of Rinko and tells her to get out of the way before Shampoo helps her do so. Rinko and Shampoo then begin insulting each other while also trying to, unsuccessfully, overtake each other. As the two ram into each other Mousse, who had managed to improve his engine's speed and performance after being spun off the road earlier, along with his convoy of other drivers (namely Ryoga, Genma and Akane) appear that got caught in front of him ram into the back of Rinko and Shampoo so they too begin being pushed.
Meanwhile, Happosai decides to use his Happo-Fire Burst in order ensure victory, however, Ranma tries to prevent this and the two begin to argue. Whilst they argue they fail to notice the large Water tower in front of them, the Hapoo-Fire Burst then explodes causing the tower to collapse, this results in all the drivers in the immediate area to crash, including Rinko. Afterwards Rinko is shocked at the damage done to her kart and the animals and is ultimately left speechless as she can only watch as Kasumi and Nabiki come in first and second place, respectively.
Rinko is one of the many guests at the Tendo family Christmas party.
Despite not having any on-screen racing other than that with Ranma and co., according to one of the Pit crew Rinko holds the current fastest lap record for the race course at the Amusement Park. It is shown that during her race with Ranma that Rinko is indeed skilled at driving and controlling the race karts used at high speeds, with only Ranma being able keep up with her (before Mousse accidentally "powers up" his kart and begins pushing everyone of course).
- I'm getting sick of being passed! - Rinko after Happosai overtakes her.
- Watch it! - Rinko after Shampoo rams into the back of her kart.
- Who does she think she is?... calling me an old lady!? - Rinko's response to Shampoo calling her an old lady.