ACR X ON APCH HAD LTSS FROM DEPARTING SAAB 340. GAR ISSUED.

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ACR X CLRED FOR AND EXECUTED AN ILS RWY 36 APCH TO DCA. WE BROKE OUT OF THE CLOUDS AT ABOUT 600 FT. BOTH THE FO AND I IMMEDIATELY SPOTTED A SAAB 340 BEGINNING ITS TKOF ROLL ON RWY 36. IT APPEARED THAT IT WAS GOING TO BE SAFE TO CONTINUE TO A LNDG. AS THE SAAB BECAME AIRBORNE THE TWR CTLR TOLD US TO GAR. WE WERE AT ABOUT 100 FT AND 1/4 MI FROM THE RWY THRESHOLD WITH THE SAAB ABOUT A MI AHEAD CLBING TOWARD OUR ALT AT A SPD MUCH SLOWER THAN OURS. I INITIATED THE STANDARD GAR PROC AND ALSO BEGAN AN IMMEDIATE L TURN TO GAIN SOME LATERAL SEPARATION BEFORE WE BOTH BECAME IMC. I ROLLED OUT ON A 320 DEG HDG AND; WITH OUR COURSES DIVERGING. WE CLBED BACK INTO THE CLOUDS. THE TWR CTLR THEN CLRED US TO INTERCEPT THE DCA 328 DEG RADIAL AND MAINTAIN 2000 FT. I TOLD THE TWR CTLR THAT WE WERE UNABLE TO INTERCEPT THE DCA 328 DEG RADIAL AND THAT I WOULD CONTINUE FLYING A 320 DEG HDG (ABOUT A MI SW OF THE DCA 328 DEG RADIAL) UNTIL SHE COULD ASSURE ME THAT WE HAD SEPARATION FROM THE SAAB. AS WE APCHED 2000 FT OUR TCASII DISPLAY SHOWED A TARGET AT 4 O'CLOCK AND 1 MI; 400 FT BELOW OUR ALT AND CLBING; WHICH I ASSUMED WAS THE SAAB. I ELECTED TO CONTINUE CLBING TO AVOID THE TARGET; AT WHICH TIME TWR CLRED US TO 3000 FT AND HANDED US OFF TO DEP CTL. THE TWR CTLR MADE A JUDGEMENT ERROR WHEN SHE CLRED THE SAAB INTO POS ON THE RWY. THERE WERE TAILWINDS OF ABOUT 30 KTS ON THE FINAL APCH DOWN TO ABOUT 1500 FT WHERE THEY SLOWLY DIMINISHED TO ABOUT 5 KTS ON THE SURFACE. ALSO; THE RWY WAS FLOODED TO THE TOPS OF THE GROOVING. THE AIRPLANE THAT LANDED AHEAD OF US USED THE ENTIRE RWY LENGTH TO STOP; WHICH LEFT MINIMAL TIME FOR THE SAAB'S DEP. THE TWR CTLR MADE A SECOND JUDGEMENT ERROR WHEN SHE GAVE US THE STANDARD GAR ROUTING WITHOUT CONSIDERING THE CLOSE PROX OF THE AIRPLANES. HAD I FOLLOWED THE TWR CTLR'S INSTRUCTIONS WE WOULD HAVE COLLIDED.