IFR ACFT X OVERDUE ACFT SEARCH.

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I RELIEVED THE APCH CTLR FROM THE APCH/DEP POS. HE BRIEFED ME ON AN IFR DEP AND DID NOT SAY ANYTHING ABOUT ANOTHER IFR ACFT INBOUND TO GJT. (I MAY NOT HAVE GIVEN HIM A CHANCE TO SAY ANYTHING BECAUSE I WAS VERY QUICK TO MENTION THE ARR). I HAD JUST GLANCED AT THE ARR AND SAW A TIME OF **18; ASSUMING IT WAS XX18Z. AT APPROX XX10Z I NOTICED THE ESTIMATED ARR WAS 2 HRS OLD. I LOOKED AT THE POS LOG TO DETERMINE WHICH CTLR WAS WORKING THE POS AND ASKED HIM IF HE KNEW WHAT HAD HAPPENED TO ACFT X. HE SAID; 'I GOT A REMOVE STRIP ON HIM AND THEN ANOTHER STRIP; BUT HE NEVER SHOWED UP. I DON'T KNOW WHAT HAPPENED TO HIM.' I IMMEDIATELY CALLED ZDV AND INFORMED HIM OF THE SIT. THE CTR CTLR SAID HE WOULD HAVE TO DO A PAPER SEARCH TO FIND OUT. ABOUT 10 MINS LATER; HE CALLED AND SAID HE COULD NOT DETERMINE WHAT HAD OCCURRED TO THE FLT BECAUSE THE FLT PROGRESS STRIPS DID NOT HAVE ANY WRITING ON THEM; AND THAT HE WOULD CALL ZLC TO CONDUCT A PAPER SEARCH ON THE ACFT. I TURNED TO ANOTHER CTLR WHO WAS WORKING THE APCH CTL POS AT THE TIME; AND ASKED IF HE KNEW ANYTHING ABOUT X. HE SAID HE DIDN'T KNOW. THE CTR CTLR CALLED ME AT APPROX XX30Z TO INFORM ME THE ACFT HAD DIVERTED TO SLC. WHILE I WAS CONDUCTING A SEARCH FOR THIS ACFT; ONE OF THE CTLRS (THERE WERE 5 OF US ON DUTY THAT DAY) SAID; 'WHO GIVES A XXXX WHAT HAPPENED TO HIM; HE PROBABLY WENT SOMEWHERE ELSE.' THERE WAS A 99.999 PERCENT CHANCE THAT ACFT WENT SOMEWHERE ELSE; HOWEVER; THERE REMAINS A .001 PERCENT CHANCE THAT ACFT COULD HAVE EXPERIENCED A SERIOUS EQUIP MALFUNCTION AND EVERYONE ON BOARD THAT ACFT COULD HAVE BEEN BURNING SOMEWHERE IN THE UTAH DESERT. COMMON SENSE AND GOOD JUDGEMENT DICTATES THAT AN ACFT OVERDUE AT ITS ESTIMATE BY MORE THAN 5 MINS; SHOULD BE IMMEDIATELY LOCATED. ESPECIALLY WHEN THERE ARE OTHER IFR ACFT UTILIZING THE SAME APCH AIRSPACE. NOT ONLY DOES THIS SIT INVOLVE COMMON SENSE AND GOOD JUDGEMENT; BUT THE CTLR ASSIGNED TO A POS HAS BEEN DELEGATED THE RESPONSIBILITY FOR ALL IFR ACFT DEPARTING; ARRIVING; AND/OR TRAVERSING HIS ASSIGNED AIRSPACE; AND SHOULD BE AWARE OF THE POS OF ALL HIS ACFT IN HIS/HER AIRSPACE AT ANY MOMENT WHILE ASSIGNED TO THAT CTL POS.