B737 AND B727 HAD LESS THAN LEGAL SEPARATION.

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WE WERE ACR FLT ABC FROM LGA TO ORD. WE FOLLOWED AN ACR FOKKER ON DEP FROM RWY 31. AN ACR B727 WAS IMMEDIATELY BEHIND US FOR RWY 31. OUR INITIAL CLRNC WAS 5000 FT AND HDG 360 DEGS. APCHING 5000 FT ATC CLRED US TO 11000 FT. AT APPROX 6000 FT ATC CLRED US TO LEVEL AT 8000 FT TURN 310 DEG HDG. AFTER LEVELING AT 8000 FT; 310 DEG HDG; OUR TCASII ADVISED OF AN ACFT BEHIND AT 7 O'CLOCK POS AT 7000 FT CLBING. AT TCASII INDICATION OF ACFT AT 7500 FT CLBING WE RESPONDING TO INITIAL RESOLUTION TO CLB. AT 8200 FT; OUR ALT; THE TFC WAS AT 7800 FT CLBING ON OUR TCASII. THE CTLR CLRED US TO 9000 FT UPON OUR NOTIFICATION OF CLBING FOR RESOLUTION. HE IMMEDIATELY DIRECTED A TURN TO 330 DEG HDG. THE ACR B727 WAS THEN VISUALLY ACQUIRED AT OUR 8 O'CLOCK POS APPROX 1 NM AWAY. THE CTLR THEN QUERIED US 'WHY DID YOU TURN OFF OF THE 360 DEG HDG?' OUR REPLY 'WE WERE TOLD TO TURN TO 310 DEG HDG.' THE INCIDENT WAS CONCLUDED AND WE WERE PASSED OFF TO ANOTHER ATC FREQ WHERE DECLARED OUR INTENT TO FILE A NEAR MIDAIR RPT. SUPPLEMENTAL INFO FROM ACN 427466: I WAS TRAINING A DEVELOPMENTAL ATCS ON LGA DEP WHILE DEPARTING RWY 31 WITH 340 DEG AND 360 DEG HDG ASSIGNED BY LGA TWR DEPENDING ON THEIR DEP SID (FIX). THE TRAINEE RESTR A B737 JET AND A B727 JET; CONSECUTIVE DEPS ON 360 DEG AND 340 DEG HDGS RESPECTIVELY; TO 8000 FT BECAUSE OF WBOUND XING TFC AT 9000 FT. THE TRAINEE TURNED THE FIRST DEP TO A 310 DEG HDG APPROX 8 MI N OF LGA; THIS HEADING CONSEQUENTLY BROUGHT THE B737 JET ON A XING OR CONVERGING HEADING WITH THE SECOND DEP THE B727 JET ON A 360 DEG HDG. THE THIRD DEP CAME OFF ON A 360 DEG HDG; A FOKKER JET; AND THE TRAINEE HAD NO FLT DATA STRIP. HE AND I MUST HAVE BECOME DISTRACTED AND I (THE TRAINER) MISSED THE '310 DEG HDG' XMISSION GIVEN TO THE B737 JET MOMENTS EARLIER. I NOTICED THE TRACK OF THE B737 JET AND B727 JET CONVERGING AND INSTRUCTED THE B737 JET TO TURN N AND THE B727 JET TO TURN WBOUND TO INCREASE THE SEPARATION. I BELIEVE WE BECAME (TRAINER AND TRAINEE) DISTRACTED WITH THE MISSING INFO. I DON'T RECALL HEARING THE TRAINEE TURN THE B737 JET OR THE B727 JETS. READBACK; HOWEVER; IT WAS CLR ON THE TAPE. THERE WAS NO BACKGROUND INTERFERENCE AT THE TIME NOR WERE WE VERY BUSY. THIS WAS JUST HUMAN ERROR!