Metallic faceted edged disc UFO following jet flying reported Bradford PA 5/20/78

In 1978 I was a student at University of Pittsburgh at Bradford and was taking a course in backpacking for 2 credits. The Instructor was driving us in a station wagon toward Allegheny St park and we were about to embark on a 10 mile hike and an overnight camp. I was looking at the sky out the window and noticed what looked like a small military jet flying in what I thought at the time was a northern direction (not at top speed but a few hundred mph) toward the Allegheny St park on our right. It left a short vapor trail behind it. What was unusual was that there appeared to be a multiple faceted metallic disk tailing it quite closely, like within 150 feet of it flying at the same speed but not leaving a trail. It seemed to have a polygonal shape with 8 to 10 sharp even length edges. The sun was out and it was mainly a blue sky. It had a shiny metallic surface. That is all the detail I could see. It looked like 3000 to 5000 feet up and it might have been 20 to 40 feet across I am guessing because I am not sure of the altitude. Anyway I shouted out "I think I see a UFO" and they all laughed as if I was nuts (a fun group of course) but my roommate who was a smart guy and was a paramedic at age 17, double checked me and immediately corroborated what I saw, "no I think that might be a UFO". Suddenly I had cried! The teacher immediately pulled the car over. Everyone wanted to see. And we all got out to look at it. The UFO actually stopped and hovered right then almost directly above us (thousands of feet up - about the size of a small aspirin 4 feet away) at that point as the jet continued flying along on its path seemingly oblivious to that there was something right behind it. Then after about 15 or 20 seconds, while the jet was still visible, this UFO Sighting slid across the sky within about 1 second (about 5 or 10 degrees) to get right back on the tail of the jet, and continued following the jet once again right on its tail and at the same lower speed of the jet. In the moment it 'slid' across the sky, it left no trail, and it was quick like only 1 second for it to travel the distance the jet had flown in probably 15 to 20 seconds. That might have been faster than or close to the speed of sound but there was no sonic boom. This all happened within about a 2 minute timespan. None of us reported this, but I seem to remember pretty clearly that I found out by either TV or a local newspaper that there were a number of UFO Sightings reports or sightings north of there, across the border in NY State on the same day we saw this thing. I don't remember the exact day but I assume it was late in the semester that year because we had to hike neck deep through a stream (so I am saying it was late May). I was only there in Bradford 2 years so it was either 1977 or 1978 and I'm thinking it was '78 but I'm not 100% on that. MUFON CMS# 77764