FLC OF A CARGO B727 INITIATED PROCS TO SLOW ACFT DURING VISUAL APCH TO PARALLEL RWYS TO PREVENT OVERTAKING AND PASSING A B757 ALSO ON A VISUAL FINAL APCH TO THE OTHER PARALLEL RWY.

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SIT OCCURRED AT ABOUT XA00Z WHILE ON APCH TO RWY 34R AT SEA ARPT. THE ACFT I WAS IN COMMAND OF WAS A B727. THIS WAS AN ACR X CARGO RUN WHICH STARTED IN IND WITH A STOP AT MSP BEFORE ARR AT SEA. WE WERE BEING VECTORED FOR A VISUAL APCH AT SE. THE CTLR CLRED ACR X TO 4000 FT ON A HDG OF 250 DEGS WITH NO RESTR IN AIRSPD. HE ASKED US IF WE HAD IN SIGHT AN ACR Y AT OUR 10 O'CLOCK POS. WE REPLIED THAT WE DID. THE CTLR THEN SAID THAT THE ACR Y FLT WAS FOR RWY 34L AND WE WERE CLRED VISUAL APCH RWY 34R. THE ACR Y B757 PASSED THROUGH OUR 12 O'CLOCK POS AND WE STARTED OUR TURN TO FINAL FOR RWY 34R. AT THIS TIME OUR INDICATED AIRSPD WAS 220 KTS AND OUR SPD SEEMED TO BE COMPARABLE. MOMENTS LATER OUR ACFT SEEMED TO BE OVERTAKING THE ACR Y B757; AT WHICH TIME THE APCH CTLR TOLD US NOT TO PASS THE B757. I INSTANTANEOUSLY DEPLOYED THE SPD BRAKES AND PUT THE GEAR DOWN TO RAPIDLY SLOW THE ACFT. AT THIS TIME I BELIEVED THIS TO BE ADEQUATE. MUCH TO MY SURPRISE; THE ACR Y B757 WAS ALSO SLOWING VERY FAST. I EXTENDED THE FLAPS AND CONTINUED TO SLOW; AT WHICH TIME THE APCH CTLR TOLD US TO CONTACT TWR. I STILL BELIEVED WE WOULD NOT PASS THE B757; BUT LATER AFTER BEING CLRED TO LAND WITH THE CONTINUED DECELERATION WE PULLED EVEN WITH THE B757 ON APCH TO PARALLEL RWYS 34R&L. WITH MY CONTINUED SLOWING THE B757 INCREASED THE DISTANCE AND WE LANDED. THIS COULD HAVE ALL BEEN AVOIDED WITH BETTER AWARENESS FROM MYSELF ON THE EVENT. IN ADDITION; A LITTLE INFO FROM THE CTLR ON THE RATE OF CLOSURE BTWN MYSELF AND THE B757. MOST OF ALL WAS THE STATE OF FATIGUE AFTER STARTING DUTY AT XX00Z AND FLYING MKE-ORD-IND-MSP- SEA WITH WX DELAYS AT NIGHT WITH ARR AT XZ03Z AT SEA.