ACR WDB ACFT OVERTAKEN DURING FINAL ON A VISUAL APCH BY ANOTHER ACR LGT ACFT ON APCH TO THE PARALLEL RWY RESULTING IN A NMAC.

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WE APCHED SEA-TAC FROM THE E TO LAND ON RWY 34. ON R BASE; APCH CLRED US FOR A VISUAL TO 34R TO FOLLOW ACR FLT WHICH WAS POINTED OUT TO US AND WE VERIFIED. ON FINAL; APPROX 2700 FT TCASII SHOWED TA AHEAD AND BELOW ACR AND UNKNOWN APPROX 8 O'CLOCK HIGHER. I HAD JUST TUNED TWR FREQ WHEN WE GOT AN RA AND SO CALLED OUT 'HE'S R BEHIND US 400 FT -- IT'S SHOWING 200 FT DSCNT.' FO PUSHED FORWARD OUT OF 2000 FT/MIN RANGE (RED); AS I LOOKED FOR ACFT. MY FIRST SIGHT OF THE LGT WAS A FEW HUNDRED FT ABOVE US; VERY NEAR OUR COURSE; A BIT BEHIND; PASSING RAPIDLY. AS ACFT CLRED; FO LEVELED OFF AND RE-INTERCEPTED GS. THE LGT ACFT PULLED AHEAD APPROX 3/4 MI THEN PUT HIS GEAR DOWN AND SLOWED TO HIS APCH SPD WHICH WAS LESS THAN OURS. WE WERE NOW OVERTAKING HIM. MEANWHILE; BACK ON 34R; THE TFC WE WERE FOLLOWING WAS VERY SLOW TO EXIT THE RWY AND TWR TOLD US TO BE READY FOR A GAR. AS WE WENT AROUND FROM APPROX 100 FT; THE ACFT THAT PASSED US WAS JUST TOUCHING DOWN. WHEN WE WENT TO APCH CTL FREQ; THEY ASKED IF WE WENT AROUND BECAUSE OF LGT OVERTAKING. THERE WAS SOME CONVERSATION AND THEY APOLOGIZED FOR NOT TELLING US ABOUT LGT ACFT FOR THE L RWY. DURING PHONE CONVERSATION WITH TWR AND APCH; I WAS TOLD THAT ACR Y WAS GIVEN A CLRNC TO MAINTAIN VISUAL CONTACT WITH US DURING HIS TURN TO FINAL. ONLY HE KNOWS HOW CLOSE HE WAS TO OUR ACFT. IT WAS TOO CLOSE FOR ME AND A GREAT DISTR ON OUR APCH. HOW CAN ANYONE MAINTAIN VISUAL SEPARATION AFTER PASSING THE OTHER?