PA28 NON ADHERENCE TO ATC INSTRUCTION OVERTOOK BE90 ON FINAL APCH. NMAC. SEE AND AVOID CONCEPT.

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UPON CONTACT WITH ADS TWR THE DUCHESS WAS TOLD 'RPT R BASE; RWY 15.' UPON REACHING BASE AND ADVISING TWR THE DUCHESS WAS INSTRUCTED 'NO; NO EXTEND DOWNWIND I HAVE 7 ACFT ON FINAL.' THE DUCHESS THEN CONTINUED N AT AN ALT OF 2000 FT MSL. AFTER A DISTANCE OF 7 NM THE DUCHESS RPTED POS (OVER THE COLONY) AND INQUIRED ABOUT THE BASE LEG. THE CTLR THEN INSTRUCTED TO TURN BASE (7 MI OUT). THE CTLR THEN STATED 'TFC; CESSNA 12-2 O'CLOCK.' UPON RPTING CONTACT WITH THE CESSNA THE CTLR CLRED THE DUCHESS TO TURN FINAL AND FOLLOW TFC. THE CESSNA WAS PROBABLY A C- 172 OR C152 AND APPROX 3-5 MI IN FRONT OF THE DUCHESS. THE DUCHESS THEN SLOWED TO 90-95 KIAS. JUST AFTER THE DUCHESS WAS ESTABLISHED ON FINAL BEHIND THE CESSNA; A RADIO CALL WAS HEARD 'PIPER CHEROKEE OVER THE COLONY LNDG WITH INFO LIMA.' THE CHEROKEE WAS GIVEN 'TFC; DUCHESS 12 O'CLOCK.' THE CHEROKEE RPTED THE DUCHESS IN SIGHT AND WAS INSTRUCTED TO FOLLOW THE TFC FOR LNDG. THE DUCHESS WAS THEN CLRED TO LAND. THE DUCHESS STILL HAD THE CESSNA IN SIGHT AND WAS FLYING A STABLE DSCNT RATE AT 90 KTS. AFTER A PERIOD OF TIME THE CHEROKEE RPTED 'LOST THE DUCHESS;' THERE WAS NO REPLY FROM THE TWR. AFTER A SHORT PERIOD OF TIME THE TWR INQUIRED OF THE DUCHESS'S POS. THE DUCHESS RESPONDED '1-2 MI FINAL.' THE TWR THEN INQUIRED OF THE CHEROKEE'S POS; THE CHEROKEE'S RESPONSE WAS NOT HEARD BY THE DUCHESS. THE TWR THEN AGAIN ASKED THE POS OF THE DUCHESS; THE DUCHESS RPTED '1 MI FINAL.' JUST AFTER GIVING THIS POS RPT; THE CHEROKEE OVERTOOK THE DUCHESS; 20-25 FT DIRECTLY ABOVE THE DUCHESS; AT ABOUT A 3 KT SPD DIFFERENCE. THE DUCHESS IMMEDIATELY TURNED L AND RPTED THE GAR TO THE TWR. THE TWR INSTRUCTED THE CHEROKEE TO CONTINUE TO LAND AND THE DUCHESS TO PERFORM A L 360 DEG TURN AND RETURN TO LAND. AN NMAC WAS NOT RPTED. THIS WAS A VERY; VERY CLOSE INCIDENT; OVER A DISTANCE OF 1-2 MI. IF EITHER ACFT HAD CHANGED DSCNT RATE; BY EVEN A SMALL AMOUNT; THESE ACFT WOULD HAVE COLLIDED.