ACR X OVERTOOK ACR Y ON DEP CLB. LTSS. SYS ERROR.

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DEPARTED ACR X OFF RWY 22L L TURN HDG 120 DEG. OBSERVED 22R ARR LNDG INSTRUCTED ACFT TO TURN OFF AND HOLD SHORT OF RWY 9L FOR DEPARTING ACFT. CLR AN LTT RWY 9L TURN R 100 DEG. ACFT DEPARTED CROSSED ARR. THEN I OBSERVED ACR X OFF 22L IN A L TURN WHICH APPEARED SHALLOWER THAN NORMAL. THEN CLRED ACR Y FOR TKOF RWY 22L TURN L 120 DEG. OBSERVED ACR Y LIFT OFF AND TURN. I IMMEDIATELY BECAME CONCERNED ABOUT THE POSSIBILITY OF NOT HAVING 3 MI LONGITUDINAL SEPARATION REQUIRED. I OBSERVED ACR X AIRSPD 180 KTS. NORMALLY THROUGH MY EXPERIENCES I KNEW ACR X AIRSPD WOULD BE BUILDING. I CONSIDERED MY OTHER OPTIONS. TURNING ACR Y L WAS NO GOOD BECAUSE OF THE 9L DEP. TURNING R WOULD PUT ACR Y IN MIDWAYS AIRSPACE VIOLATING A TWR ORDER. I OBSERVED SPACING TO BE A 'TIGHT' 3 MI. ACR Y WAS LEAVING MY AIRSPACE. I DECIDED ACR X WOULD BE BUILDING HIS SPD AND SEPARATION WOULD INCREASE. I SHIPPED ACR Y. I CONTINUED TO MONITOR THE SITUATION. ACR Y SPD INCREASED DRAMATICALLY. ACR X SPD REMAINED THE SAME. LOSS OF SEPARATION OCCURRED. I RPTED IT TO THE SUPVR.