CLE APCH CTLR EXPERIENCED OPERROR AT APPROX 5000 WHEN SECOND ACFT BEING VECTORED TO FINAL OVERTOOK FIRST ACFT; CITING PLT ERROR AS CAUSE.

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I WAS WORKING THE FINAL ON THE INNER LOW POS. RWY 24R IN USE. ACR X WAS HANDED OFF TO ME FROM THE ARR OVER CTLR AT 7000 FT; 210 KTS. ACR Y WAS HANDED OFF TO ME LEAVING THE CHARDON VOR (CXR) ON A 290 DEG HDG LEAVING 9000 FT FOR 7000 FT AT 210 KTS. BOTH ACFT WERE 25 MI APART ON INITIAL CONTACT. THE FINAL WOULD SOON REACH 25 MI WITH ACR Z TRAILING ACR Y AND ADDITIONAL TFC ON THE DOWNWINDS. WHEN BOTH ACFT CHKED IN; I DSNDED ACR X TO 4000 FT AND ACR Y TO 5000 FT. 20 MI NE OF CLEVELAND HOPKINS; I TURNED ACR X TO A 140 DEG HDG AND NOTICED THAT HIS SPD WAS FASTER THAN THE TFC I RAN ON AN EARLIER SESSION. THAT IS WHEN I NOTICED ACR X WAS STILL AT 210 KTS; SO I REDUCED HIM TO 170 KTS. I TURNED ACR Y TO A 320 DEG HDG AND OBSERVED ACR X LEAVING 5000 FT AND ACR Y LEAVING 6500 FT. I OBSERVED ACR X WAS NOW DOING 230 KTS ON A R BASE AND I TOLD HIM TO EXPECT VECTORS ACROSS THE LOC FOR SPACING; AND THAT I NEEDED THE SPD (170 KTS) NOW. ACR X STATED 'I'M AT IT.' I OBSERVED THAT HE LEVELED OFF FIRST AT 4400 FT AND THEN ONCE AGAIN AT 4200 FT. I TOLD ACR X TO TURN R HDG 270 DEGS AND JOIN THE LOC. THEN; I ISSUED A SPD RESTR TO AN ACR A JET. SOMEONE OVER THE FREQ SAID MY XMISSION WAS BLOCKED. I STARTED TO REISSUE THE RESTR TO ACR A WHEN I NOTICED ACR X WAS STILL ON A BASE LEG AND STILL AT 4200 FT. I AGAIN ISSUED ACR X TO TURN TO A 270 DEG HDG AND JOIN THE LOC. THAT IS WHEN I OBSERVED ACR X STARTING HIS TURN; AND IT CORRESPONDED WITH THE DATA READ OFF. HOWEVER; SEPARATION WAS LOST; 2.75 NM/800 FT. I BELIEVE THIS WAS PLT ERROR/DEV. 1) I DON'T BELIEVE ACR X WAS AT 170 KTS WHEN HE STATED HE WAS AT IT. 2) DATA SHOWS ACR X STILL ON A BASE HDG 10 SECONDS AFTER I TOLD HIM THE FIRST TIME TO TURN AND JOIN THE LOC. 3) IT TOOK ACR X 2 MINS 50 SECONDS TO DSND FROM 5000 FT TO 4000 FT.