A B737-300 FLT CREW; WHILE OPERATING WITH ONLY 1 PACK; EXPERIENCES A FAILURE OF THE OTHER PACK.

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WE DEPARTED MCI OPERATING UNDER MEL 21-1; SINGLE PACK OP. THE R PACK WAS WRITTEN UP INOP THE PREVIOUS DAY. DURING CRUISE FLT AT FL240; APPROX 135 NM N OF AMA; WE NOTICED A PACK TRIP OFF LIGHT ILLUMINATED AND THAT THE CABIN ALT WAS ASCENDING AT A RAPID RATE. WE DONNED THE OXYGEN MASK AND INITIATED A RAPID DSCNT TO 10000 FT MSL. WE TRIED TO GET THE L PACK TO RESET; BUT IT WOULD NOT REMAIN OPERATIONAL. WE GOT THE CABIN ALT STABILIZED AT 10000 FT MSL AND TURNED TO AMA. WE TRIED NUMEROUS TIMES TO REACH DISPATCH AND AMA OPS WITH NO SUCCESS. WE HAD ZAB CALL DISPATCH TO INFORM THEM OF OUR PROB AND DIVERSION TO AMA. SHORTLY AFTER THE CTR CALL REQUEST TO DISPATCH; ANOTHER COMPANY FLT ON COMPANY FREQ CALLED DISPATCH FOR A RELAY AS WELL. APPROX 35 NM FROM AMA; WE ESTABLISHED CONTACT WITH DISPATCH AND AMENDED THE RELEASE TO SHOW AMA AS THE DEST. WE RAN THE CHKLIST FOR DEPRESSURIZATION; DUAL PACK FAILURE PRIOR TO LNDG. DURING THE DSCNT; THE FLT ATTENDANTS NOTICED THE RAPID DSCNT AND CALLED THE COCKPIT; BASICALLY SHORTLY AFTER WE PUSHED OVER TO GO DOWN. THE FLT ATTENDANTS REMAINED CALM AND PROFESSIONAL DURING THE EVENT AND KEPT THE PAX CALM AS A RESULT. WE MADE A COUPLE OF PA'S ENRTE TO AMA TELLING THE PAX OF OUR PROB; DIVERSION AND STRESSING EACH TIME THAT THE PROB WAS UNDER CTL AND THE ACFT WAS SAFE FOR FLT. COMPANY MECHS MET US AT ARR AND FIXED BOTH PACKS AND WE DEPARTED. ALL OF THE PAX SEEMED CALM AND NONE EXPRESSED ANY ANXIETY OR RESERVATION OF RE-BOARDING FOR THE REST OF THE FLT. THE EVENT WORKED OUT VERY WELL DUE TO THE VERY PROFICIENT FO AND CABIN CREW WORKING IN AN OUTSTANDING MANNER. IN HINDSIGHT; WE NEVER DECLARED AN EMER. ATC IMMEDIATELY GAVE US THE LOWER ALT DURING THE DSCNT AND AFTER THINGS HAD CALMED/SLOWED DOWN ASKED IF WE WANTED TO DECLARE AN EMER AND I ELECTED AT THAT POINT TO DECLINE. I NOW WISH WE HAD DECLARED AN EMER DURING THE INITIAL LOWER ALT REQUEST. I KNOW THAT ACAR'S IS BEING INTRODUCED ONLINE AND THE SOONER THE BETTER; FOR IT WOULD HAVE HELPED FREE UP A LOT OF TIME AND COCKPIT ATTN DURING OUR PROB.