Wow. was it that long ago? It's like nobody even remembers reel-to-reel!
Half-inch tape was an exception. It was used in some recording studios. Regular audio tape was 1/4", and that was good enough for home, radio, etc. Reels were 3, 5, 7 and 10 inches, with portables using 3 and 5 max, most machines using 7" reels. Also the tape was 1/2 mil, 1 mil and 1.5 mil. Thicker tape was more trouble-free but not as much of it fit on a reel. 1/2 mil tape could do 2 hrs on one side of a 7" reel but it was so thin it sometimes stretched.
Then tape was 4-track. That meant stereo in each direction, or you could put four separate monophonic tracks on the tape.
200 minutes is 3 hrs 20 min. At broadcast quality, stereo 7 1/2 inches per second, on 1 mil tape, in one direction, that would fill 3 1/3 7" reels. At home, in mono, at 3 1/4 inches per second, you could fit it all on one 7" reel.
Now that's for 1/4" tape. I suspect early 1/2" tape (analog) moved 15" per second. A 10" reel might do an hour (I'm guessing). But 1/2" tape went digital, and digital 1/2" tape could hold a lot more.