MD82 FLC UNDERESTIMATE ACFT PERFORMANCE CAPABILITY AND MISS XING RESTR AND CONFLICT WITH ANOTHER ACFT.

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WE DEPARTED LAS ON THE MEAD 2 SID; PEACH SPRINGS (PGS) TRANSITION. APCHING OUR ASSIGNED ALT OF FL290 AT PGS; WE WERE ASKED IF WE COULD BE LEVEL AT FL330 IN 3 MINS OR LESS; IF SO CLRED. WE SAID YES AND WERE CLRED TO FL330 TO BE 'LEVEL IN 3 MINS OR LESS.' I CONTINUED THE CLB AND AS WE APCHED THE VOR AT FL292; WE WERE RECLRED TO 'CROSS 10 DME E OF GPS AT FL330;' WHICH WE ACKNOWLEDGED. I IMMEDIATELY INCREASED THE CLB RATE; BUT SOON DISCOVERED I COULD NOT SUSTAIN THE NECESSARY CLB AND MAINTAIN ACCEPTABLE AIRSPD. A DECREASE IN CLB RESULTED IN OUR XING THE 10 DME POINT AT FL327. THE CTLR QUERIED US ABOUT OUR MODE C; AND WE RPTED APCHING FL328; THE TFC IN SIGHT; LOW AT 1 O'CLOCK POS (NO FACTOR); AND THAT WE WERE SLOW. THE TFC WAS NEVER RPTED TO US AND NO TCASII TA WAS RECEIVED. SHORTLY THEREAFTER; THE CTLR ADVISED US THEY HAD HAD A LOSS OF SEPARATION ALARM AND A PHONE CALL TO ZLA WOULD BE REQUIRED. HINDSIGHT BEING A GREAT TEACHER; WE NEVER SHOULD HAVE ACCEPTED THE INITIAL CLRNC TO FL330. ONCE CLRED; WE NEVER SHOULD HAVE ACCEPTED THE INITIAL CLRNC TO FL330. ONCE CLRED; WE NEVER SHOULD HAVE ACCEPTED A CHANGE OF CLRNC; AND FINALLY; HAVING DONE THAT; WE SHOULD HAVE GIVEN UP TRYING TO MAKE IT; AND RPTED WE MIGHT NOT MAKE FL330 BY 10 DME IN A TIMELY MANNER. CONTRIBUTING FACTOR: THE CHANGE OF A WORKABLE CLRNC TO ONE THAT PROVED UNWORKABLE. SUPPLEMENTAL INFO FROM ACN 504706: MY JUDGEMENT OF THE ACFT PERFORMANCE CAPABILITIES AND LIKELIHOOD OF REACHING THE XING RESTR WERE; OBVIOUSLY; IN ERROR. COULD HAVE AVOIDED THE CONFLICT BY NOT ACCEPTING THE CLRNC INITIALLY; OR AT LEAST REJECTING THE AMENDED CLB CLRNC. AND; AS A MINIMUM; I SHOULD HAVE NOTIFIED ATC OF THE DECREASED CLB AND THAT WE MIGHT NOT MEET OUR CLB RESTR. I WILL CERTAINLY TAKE A LITTLE MORE TIME TO CONSIDER CLB/DSCNT CAPABILITIES BEFORE ACCEPTING THAT TYPE OF CLRNC IN THE FUTURE.