ZFW CTLR EXPERIENCED OPERROR WHEN ESTIMATED CLB RATES; TIME FACTORS AND TURNS WERE MISJUDGED AND SEPARATION WAS LOST AT FL340.

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DA50 CHKED ON TXK-HI FREQ CLBING TO FL230 REQUESTING FL370. I WAS WORKING TXK-HI RADAR POS AND CLBED DA50 TO FL370. DA50 HAD DEPARTED DFW AND WAS TO OVERFLY TXK J42. AT XA26Z ACFT Y CHKED ON FREQ LEVEL AT FL340. ACFT Y WAS ENTERING THE NE CORNER OF THE SECTOR FLYING OVER TXK.C2Y.SAT. I SAY THAT A RESTR WOULD BE NECESSARY TO ENSURE DA50 WOULD GET ABOVE ACFT Y. I ASKED IF DA50 COULD BE ABOVE FL350 WITHIN 3 MINS. I HAD CALCULATED THAT SEPARATION WOULD BE LOST IN ABOUT 4 MINS. DA50 REPLIED THAT HE COULD BE ABOVE FL350 WITHIN 3 MINS. I THEN ISSUED THE RESTR TO DA50 TO BE AT FL350 WITHIN 3 MINS OR LESS. DA50 READ BACK THAT HE WOULD BE LEVEL AT FL350 IN 3 MINS OR LESS AT XA28:40. AT ABOUT XA31Z; I REALIZED THAT DA50 WOULD NOT MAKE THE RESTR AND TURNED DA50 20 DEGS R. I THEN TURNED ACFT Y 20 DEGS R. I THEN TURNED DA50 FURTHER R TO HDG 100 DEGS. THEN I TURNED ACFT Y TO HDG 300 DEGS. AT XA32:13 I TOLD DA50 TO RPT REACHING FL350. AT XA32:17 SEPARATION WAS LOST. AT XA32:29 DA50 RPTED LEVEL. I THEN CLRED EACH ACFT BACK ON COURSE. DA50 WAS APPROX 50 SECONDS LATE MEETING THE RESTR. HAD DA50 MET THE RESTR; NO ERROR WOULD HAVE OCCURRED.