The head of navigation of the Mississippi River depends on the type of craft and on the source you look at. For large oceangoing ships, it seems to be Baton Rouge, but otherwise, seems to be the Coon Rapids Dam in Coon Rapids, Minnesota, or perhaps Minneapolis-St. Paul, which is quite close by. According to Wikipedia, that's about 850 miles.
In a 40-foot schooner with oars rather than motor as the secondary propulsion, how long would it take to sail that distance upriver?
(This is for a story set in preindustrial times, hence no motor. According to Wikipedia, before the Coon Rapids Dam was built in 1913, steamboats could occasionally go upstream as far as Saint Cloud, Minnesota, depending on river conditions, but that's not a big difference. At any rate, I'm not concerned about bridges and dams as obstacles, but about considerations like river width and current.)
According to the answers to Is the head of navigation same for sailing and motorboats? the head of navigation for a sailing boat can be somewhat more restrictive than a motor boat, because of the need for a deeper keel. But for a river the size of the Mississippi, it should still be most of the way up?
I'm pretty sure it's not correct to just divide the distance by the average speed of a sailing boat. For one thing, the current will be against you all the way. For another, the number of days on which you can productively sail, might be less on a river, if having to stay within the confines of the river, restricts tacking? But that might not be a consideration on a wide river like the Mississippi? But it might become one as the river narrows as you go upstream?
If it makes a difference, the trip would take place in June. I think that's a positive, from the perspective of spring/summer rain/snowmelt making the river deeper?