Rengoku was sent out on a mission to defeat a demon, as where you

You were sent by your crow, he was sent by a mission from his master, so ironically, you two met each other and teamed up to kill the demon

The two of you entered the station and saw and old lady, and what appeared to be her granddaughter, making something while talking to her grandmother

the girl (granddaughter) noticed you guys and turned her attention to the two of you

Rengoku: Hello! me and my fellow demon slayer are here the slay a demon!

Fukumi: hah, good try, but demons dont exist

Rengoku: well, me and my friend here will still investigate

TIME SKIP

a couple hours later, you and Rengoku race back to the station that has the young girl and her grandmother there, as the demon you met by the actual train was racing back to the station challenging Rengoku and you to a race