C172 IN POS OF RWY 17 AT JYO IS UNAWARE OF A CITATION JET ON FINAL; RESULTING IN A GAR FOR THE JET.

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I WAS PROVIDING IFR TRAINING; AND ON THE GROUND AT JYO GAINING IFR CLEARANCE WHILE LISTENING TO UNICOM SIMULTANEOUSLY. UPON COMPLETION OF GAINING CLEARANCE UNICOM WAS MONITORED FOR APPROX 20 SECONDS. MY STUDENT AND I LOOKED FOR TFC ON FINAL AND SAW NOTHING. MY STUDENT ANNOUNCED WE WERE TAKING THE ACTIVE. FIVE SECONDS LATER I HEARD AN INAUDIBLE XMISSION ON THE UNICOM FREQ AND THOUGHT NOTHING ABOUT IT AT THE TIME. WE TAXIED INTO POS FOR TKOF. AS SOON AS FULL POWER WAS DEVELOPED THE CITATION JET OVER FLEW OUR ACFT TO THE R AND ANNOUNCED 'CITATION GAR.' ANOTHER PARTY ANNOUNCED; 'WE TRIED TO TELL THEM' I LOOKED AT MY STUDENT AND HE LOOKED AT ME. OUR FLT LASTED 2 HOURS MOSTLY IN IMC. THE CONTRIBUTING FACTORS WERE EVEN THOUGH WE WERE LISTENING TO UNICOM WHILE GAINING OUR CLEARANCE WE HEARD NO TFC ON BASE OR FINAL. WE DID NOT SEE ANY TFC ON FINAL PRIOR TO TAXING TO THE RWY FOR TKOF. WE HEARD NOTHING AFTER WE ANNOUNCED OUR INTENTIONS TO TAKE THE ACTIVE RWY. WE DISCOVERED WE MOVED ONTO THE RWY WHILE THE CITATION WAS ON FINAL ONCE THE JET OVER FLEW US AND ANNOUNCED GAR. THE SITUATION COULD HAVE BEEN AVOIDED IF WE HAD HEARD A JET WAS ON FINAL. ALTHOUGH I DID NOT THINK ABOUT IT AT THE TIME I LATER FIGURED OUT THAT THE PLT OF THE JET AND AN ACFT ON THE GROUND COMMUNICATED AT THE SAME TIME BLOCKING EACH OTHERS XMISSION HENCE NOT WARNING US ABOUT THE JET AFTER WE MADE OUR ANNOUNCEMENT. I PRESUME THE JETS RATE OF SPEED AND POS IN THE PATTERN ALONG WITH ATMOSPHERIC CONDITIONS CREATED THE SIT OF MAKING THE JET NOT VISIBLE TO BOTH MY STUDENT AND I. ADDITIONALLY; THE 3 MINUTE WINDOW GIVEN TO US BY ATC TO GET RELEASED MAY HAVE CAUSED A HURRIED SIT IN DEPARTING JYO. HOWEVER IT WAS MY BELIEF THAT WE LOOKED SUFFICENTLY FOR TFC AND LISTENED ENOUGH ON UNICOM TO BE AWARE OF TFC; AND THAT WE MADE APPROPRIATE DECISIONS. UNIQUELY ENOUGH THE JET PLT TOOK THE OPPORTUNITY TO 'SHOW BOAT' BY PERFORMING A LOW PASS AND 90 DEGREE SHARP TURN MID FIELD TO ENTER DOWNWIND. I WAS LATER INFORMED THAT THE CITATION CURVED AROUND TO LAND AND WAS OVER THE NUMBERS AS WE WERE UPWIND MIDFIELD; LEADING ME TO BELIEVE; THEN PERHAPS THE JET PLT HASTENED HIS DOWNWIND TO FINAL INITIALLY MAKING IT DIFFICULT FOR US TO SEE HIM TO BEGIN WITH. WE COULD HAVE AVOIDED THIS BY STOPPING THE ACFT ONCE I HEARD THE STEPPED ON XMISSION AND BY TAKING MORE TO LISTEN TO UNICOM. ALSO I WISHED ATC WOULD GIVE MORE TIME THAN 3 MINUTES TO GET OFF THE GROUND TO GIVE MORE TIME TO DEPART ARPTS IN UNCONTROLLED ENVIRONMENTS. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR INDICATED THAT BECAUSE OF THE 3 MINUTE WINDOWS HE HAD ON HIS CLEARANCE VOID TIME; HE FELT RUSHED. IN THE FUTURE; RPTR SAID THAT HE WILL ASK ATC FOR MORE REALISTIC WINDOWS TO ACCOMMODATE HIS NEEDS.