AN E120 CREW IN DSCNT TO SLC; SLOWED 45 KTS BELOW THE SPD ATC THOUGHT THEY WERE MAINTAINING.

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ON THE SPONE ARR INTO SLC FROM GJT WE WERE EXPERIENCING LIGHT TURB AT OUR CRUISING ALT. JUST AS WE WERE GOING TO ASK FOR HIGHER WE WERE INSTRUCTED TO CROSS SPONE INTXN AT 16000 FT. INSTEAD OF ASKING FOR HIGHER WE STARTED A MORE GRADUAL DSCNT. SHORTLY AFTER; WHILE IN THE DSCNT; ATC QUERIED OUR SPD. THE CAPT REPORTED '210 KTS IN THE DSCNT.' BEFORE HE ASKED US HE HAD REPORTED TO ANOTHER ACFT TO EXPECT LIGHT TO MODERATE TURB THROUGH THE ENTIRE DSCNT. THE CTLR TOLD US THAT HE KNEW IT WAS TURBULENT AND THAT IF WE COULD MAINTAIN BEST FORWARD SPD. WE CONTINUED TO DSND AT APPROX 210 KTS WHICH IS SLOWER THAN NORMAL; BECAUSE OF BOTH THE LIGHT TURB WE WERE IN AND BECAUSE OF POTENTIAL MODERATE. THE DSCNT CONTINUED FOR AWHILE AND AS I LEVELED I INADVERTENTLY ALLOWED THE ACFT TO SLOW FROM 210 KTS TO ABOUT 165-170 KTS (VB 175 KTS) SINCE I HAD NOT ADDED PWR SOON ENOUGH THIS HAPPENED. AFTER A SHORT TIME I NOTICED THE SPD AND ADDED THE PWR FOR CRUISE AT THAT ALT. WHEN SPD REACHED 185 KTS ATC QUERIED OUR SPD. AFTER REPORTING 185 KTS HE RECOMMENDED THAT IF WE WERE GOING TO SLOW WE NEEDED TO LET THEM KNOW AND THAT IF WE ARE ASSIGNED 210 KTS (WE WERE NOT) WE NEED TO TELL THEM IF WE CAN'T. I AM NOT SURE WHY; BUT HE WAS VERY RUDE FROM THE BEGINNING. THE CAPT TOLD HIM WE WERE IN TURB HOWEVER SHE DID NOT REALIZE THE ERROR ON MY PART AND MUST HAVE ASSUMED I WAS SLOWING FOR THE BUMPS.