Language proficiency per week of downtime

One of my players does not speak common as they come from a village the speaks entirely elvish. We are coming up on a couple weeks of downtime in the campaign and another one of the players wants to teach them common. According to the Xanthar’s rules it takes 10 weeks to become proficient in a language, but they would learn some over a couple weeks. My question is how much of a language would a character pick up in that time span? How would they role play speaking common with a limited knowledge?