Ragtime main theme vs Solace by Scott Joplin

Today while watching MAS*H (specifically 4x13 The Gun), I heard Father Mulcahy in the background play a ragtime song on piano and I was like, what is this, it sounds so similar to the main theme from Ragtime? Turns out (thanks imdb) it's Solace by Scott Joplin. Listening to it, not the whole song but the main theme of it sounds soooo similar to the main Ragtime theme which I think is so cool. Go take a listen if you haven't heard of it!

I was just wondering if anyone knew of this connection, or if the composers intended it this way or such, especially because Coalhouse is stated as being a student of Scott Joplin. I had pretty much only ever heard Maple Leaf Rag and The Entertainer from Joplin so I'm not super knowledgeable