CLOSE PROX CPR SMT AND GA SMT ON LOC TO CDC A NON TWR ARPT.

Narrative

WE WERE APPROX 17 MI NE OF CDC ON A VISUAL APCH. WE HAD CANCELLED IFR; VISIBILITY WAS GOOD; WE WERE FAMILIAR WITH THE ARPT AND HAD THE RWY IN SIGHT. CDC UNICOM INFORMED US THAT RWY 20 WAS IN USE; R TFC; ALSO AN SMT Y; WAS IN THE AREA MAKING INST APCHS. MY CO-CAPT WAS FLYING AND I FIGURED HE WOULD FLY TO THE ARPT AND ENTER R DOWNWIND FOR RWY 20; AS USUAL. THE SMT Y THEN CAME ON UNICOM AND SAID HE WAS ON A 10 MI FINAL FOR RWY 20 ON THE ILS. MY CO-CAPT THEN REMARKED THAT THE SMT Y WAS WELL AHEAD OF US AND THAT HE WAS GOING TO FOLLOW THE SMT Y IN ON THE ILS. I CONCURRED SINCE THIS PROC SEEMED TO PROVIDE THE LEAST AMOUNT OF TFC CONFLICT. WE WERE BOTH LOOKING FOR THE SMT Y. I TUNED IN THE ILS AND INFORMED UNICOM WE WERE PLANNING TO LAND #2 BEHIND THE SMT Y. WE WERE JUST INTERCEPTING THE FINAL COURSE; APPROX 7 MI OUT; WHEN THE SMT Y SAID 'TFC LNDG AT CEDAR CITY; YOU JUST BLEW PAST US!' I ASKED HIM IF HE WAS TALKING TO THE SMT X AND HE REPLIED AFFIRMATIVE. HE ASKED US IF WE HAD SEEN HIM AND I REPLIED NEGATIVE. AFTER THE SPLIT SECOND OF TERROR HAD CLRED; WE DECIDED TO CONTINUE ON SINCE WE WERE #1 NOW. THE SMT Y BROKE OFF THE APCH AND CIRCLED FOR ANOTHER ONE. WHEN WE TURNED OFF THE RWY; THE SMT Y ASKED US IF WE HAD HEARD HIM SAY HE WAS ON A 10 MI FINAL AND I REPLIED AFFIRMATIVE BUT MY CO-CAPT SAID HE HAD HEARD IT WAS A 2 MI FINAL. I APOLOGIZED TO THE SMT Y SAYING WE BOTH HAD THOUGHT THAT THEY WERE WELL AHEAD OF US. IT IS EXTREMELY UNNERVING TO THINK YOU COULD PASS AN ACFT ON AN ILS AND NEVER SEE IT. MY CO-CAPT AND I WERE PROBABLY IN A MIND SET THAT WE KNEW WHERE THE SMT Y SHOULD HAVE BEEN. WE CONFINED OUR SCAN TO THAT AREA RATHER THAN CONSIDERING OTHER POSSIBILITIES. LNDG PREPARATION ALSO HAMPERED OUTSIDE SCANNING. FOR US TO CONTINUE INTERCEPTING THE ILS WITHOUT HAVING THE OTHER ACFT IN SIGHT; WAS QUITE NAIVE. HOW WE CAUGHT THE OTHER ACFT SO FAST IS STILL A MYSTERY. ONE FACT IS FOR SURE; OUR ASSUMPTION OF WHERE THAT ACFT WAS OR SHOULD HAVE BEEN COULD HAVE BEEN DISASTROUS. AS A SIDE NOTE OUR SMT X ALONG WITH THE SMT Y HAVE EXCELLENT FORWARD FACING RECOGNITION/LNDG LIGHTS; BUT MINIMAL REAR FACING LIGHTING AS DOES OTHER ACFT. SPOTTING AN ACFT FROM THE REAR CAN BE DIFFICULT AS EVIDENCED HERE. WE SHOULD HAVE STAYED WITH OUR ORIGINAL PLAN OF GOING TO THE ARPT ENTERING THE PATTERN THUS GIVING US MORE TIME TO LOOK THINGS OVER AND SORT THINGS OUT.