A WESTWIND 24 FO SET AN EXPECTED CLB TO ALT IN ALT ALERTER. CAPT CONFIRMED AND BEGAN CLBING. ATC QUESTIONED CREW AND TOLD THEM TO EXPEDITE TO EXPECTED ALT.

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ON A PAX PART 135 TRIP DURING DEP CLB PHASE OF FLT; I (THE PF) AND TRIP ASSIGNED PIC WAS LOOKING AT OUR DEST NON-CTLED ARPT DATA/INFO. WHILE AT FL310(?) WE WERE GIVEN AN 'EXPECT' TO CLB CLRNC TO FL340. THE PNF ANSWERED FL340. I HEARD THE SIC SAY FL340 AND SET NUMBER IN THE ALT ALERTER AND COMMENCED A CLB TO FL340. I BELIEVE I HEARD THE CTLR SAY EXPECT; BUT WHEN I SAW THE PNF SET THE ALT; I CONFIRMED FL340 WITH HIM AND HE ACKNOWLEDGED. ATC ASKED IF WE WERE CLBING AND THE SIC REPLIED YES WE CLRED TO FL340. ATC SAID IT WAS AN EXPECTED ALT; AND CONTINUE AT A GOOD RATE. UPON REACHING THE ALT; WE WERE GIVEN A FREQ CHANGE AND I TOLD THE SIC/PNF TO ASK IF THERE WAS A PROB -- NO; BUT IT WAS CLOSE. I FEEL THAT IT IS THE INABILITY OF THE SIC TO HEAR RADIO CALLS. THE LAST TIME WE FLEW THE EXACT SITUATION HAPPENED. WE WERE GIVEN AN EXPECT ALT; BUT THE SIC SET THE ALT IN THE ALERTER. WE ARE BOTH PIC'S IN THE ACFT. FROM NOW ON I AM GOING TO VERIFY THE ALT WITH HIM BEFORE HE SETS IT IN THE ALERTER. HE IS IN HIS LATE 50'S AND HAD BEEN A CONSTRUCTION WORKER PRIOR TO HIS FLYING CAREER; WHICH I THINK HAS LED TO HIS INABILITY TO HEAR.