ACR LTT UNABLE TO CLIMB TO OR MAINTAIN REQUESTED AND ASSIGNED ALT HAD LESS THAN STANDARD SEPARATION WITH ENROUTE LTT.

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AT XA20 UCT IN CRUISE FLT AT FL270; MSO TO SLC. AFTER CHKING THE APPROPRIATE PERFORMANCE CHARTS; I REQUESTED AND RECEIVED A CLRNC TO FL290 TO TOP CLOUDS AHEAD. AT APPROX XA24 WE REACHED 28900' AND COULD NOT CLB ANY HIGHER. THE RATE OF CLB WENT FROM ZERO TO A SLOW DSCNT. THE CTLR ASKED US WHAT OUR ALT WAS; WE ADVISED HIM WE WERE AT 28600' AND COULD NOT CLB TO FL290; AND REQUESTED A CLRNC TO FL270. THE AIRPLANE STOPPED DSNDING AT 28500'. ABOUT 30 SECS LATER WE PASSED THE METEOROLOGICAL CONDITIONS WHICH TOOK OUR CLB PERFORMANCE AND RESUMED A VERY SLOW CLB. AT THE POINT OF REACHING 28700' AGAIN THE CTLR CLRED US TO FL270. THE CTLR ADVISED US THAT ATC'S EQUIP REGISTERED A CA WITH AN LTT Y JET AT FL280. WE WERE NOT ABLE TO CLB ABOVE 28700' AND WE THOUGHT CENTER SAW THIS ON THEIR SCREEN. AFTER WE LANDED IN SLC THE SUPVR TOLD ME THEIR EQUIP SHOWED US AT FL290 AND THIS WAS THE REASON NO VECTOR WAS GIVEN TO THE LTT Y. IN RETROSPECT THE CTLR'S EQUIP SHOWED A VERY SLOW RATE OF CLB ABOVE FL280 FOR US. POSSIBLY THIS COULD HAVE ALERTED HIM TO THE NEED FOR A VECTOR. MANY TIMES IN CRUISE FLT WE RECEIVE VECTORS AWAY FROM ACFT WHICH ARE MUCH FARTHER AWAY THAN THE LTT Y IN THIS SITUATION.