LESS THAN STANDARD SEPARATION WHEN APCH CTLR FAILED TO APPLY VISUAL SEPARATION AND ISSUE APCH CLRNC BEFORE ACFT ON CONVERGING COURSES CONFLICTED AT SAME ALT.

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OUR FLT; LGT X; WAS ON LEFT PARALLEL DOWNWIND TO RWY 24L AT SLC. WE WERE CLRED FROM 9000 TO 7000'; AND A LEFT TURN FROM ASSIGNED HDG OF 155 DEGS TO 070 DEGS. IN THE DSCNT WE WERE CLRED TO 6500'. ALL 3 CREWMEMBERS NOTICED AN ACFT APCHING FROM THE S AND MADE COMMENTS AS TO IT POSSIBLY BEING CONFLICTING TFC. WE WERE UNABLE TO COM WITH APCH BECAUSE OF FREQ CONGESTION. ATC GAVE US NO CHANGE OF HDG OR INSTRUCTIONS TO INTERCEPT THE LOC. THE OTHER ACFT; LGT Y; APPEARED TO BE AT OUR ALT AS WE APCHED 7000' IN OUR DSCNT TO 6500'. IT ALSO BECAME APPARENT THAT WE WERE ON A NEAR PERPENDICULAR COLLISION COURSE (NO CHANGE IN RELATIVE BEARING) WITH LAT SEP DECREASING VERY RAPIDLY. LGT Y; BY THIS TIME; HAD MANAGED TO ALERT APCH; WHO GAVE THEM A TURN TO 020 DEGS. WE WERE NOW BELOW 7000' AND CONTINUED OUR TURN BEYOND 070 DEGS TO ASSURE SEP. ATC THEN CLRED US FOR VISUAL TO RWY 34L; WHERE WE LANDED W/O INCIDENT AFTER CORRECTING BACK TO THE W. LGT Y LANDED RWY 34R AFTER WE TURNED OFF. UPON TALKING TO LGT Y'S CAPT ON THE GND; WE FOUND THAT ALTHOUGH CLRED TO 7000'; ATC THOUGHT HE TO BE AT 8000'. AT THE TIME OF THIS RPT; I HAVEN'T FOUND WHY WE WEREN'T CLRED FOR SOMETHING OTHER THAN 070 DEG HDG. ALTHOUGH AT NO TIME DO I FEEL WE WERE LESS THAN 500' HORIZ; OUR CONVERGENCE RATE WOULD HAVE REDUCED TO THAT IN A FEW SECS. I WOULD ESTIMATE 0' HORIZ WOULD HAVE OCCURRED IN APPROX 5 SECS HAD THERE BEEN NO TURNS. SLC RWY 34'S HAVE EXTENDED CENTERLINES THAT CONVERGE SOMEWHERE AROUND THE OM. THERE IS AN 05 DEG (IF MEMORY SERVES) DIFFERENCE IN MAGNETIC RWY HDG. PERHAPS A CHARTED VISUAL TO RWY 34R WITH AN OFFSET FINAL IS NEEDED. THIS WOULDN'T HAVE CHANGED OUR SITUATION (AN ATC PROB); BUT MAY CHANGE ONE IN THE FUTURE.