ACR DSNDS TO MDA 16 MI EARLY ON APCH TO RWY 3R AT DTW.

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WX IN DTW. BRAKING ACTION POOR. RWY 3L APCH IN USE; RWY 3R CLOSED. RWY 3L GS OTS. FLYING INTO DTW; I WAS FLYING AND WE WERE BEING VECTORED BEHIND A HVY B757; 20-25 MI OUT FOR A LOC ONLY APCH TO RWY 3L. ONCE ESTABLISHED ON THE APCH TO RWY 3L; WE WERE GIVEN A BRAKING ACTION RPT OF POOR AND SINCE I WAS A NEW FO WITH LESS THAN 100 HRS IN TYPE; THE CAPT HAD TO DO THE LNDG. AT THIS TIME; THE TWR ADVISED THE B757 AND US THAT RWY 3R WAS AVAILABLE WITH GS. THE B757 DECLINED AND WE ACCEPTED. THE TWR GAVE US AN INTERCEPT HDG AND THE ILS FREQ. HE ALSO HAD US DSND TO 3000 FT. WHILE XFERRING THE ACFT; SETTING UP AND IDENTING FREQS; GETTING APCH PLATES OUT AND ALSO SWITCHING AUTOPLTS; WE WERE NEEDLESS TO SAY VERY TASK SATURATED. THE CAPT INTERCEPTED THE LOC AND AT THIS POINT WE NOTICED WE HAD NO GS INFO. WE DECIDED TO DO A LOC APCH AND DSNDED TO LOC MINIMUMS BASED ON OUR DME INDICATION. THE TWR AT THIS TIME GAVE US A LOW ALT ALERT. WE ADVISED HIM THAT WE WERE DOING A LOC ONLY APCH AND THAT WAS THE REASON FOR THE LOW ALT. ON THE DSCNT TO LOC MDA; WE WERE CLR OF CLOUDS WITH ADEQUATE VISIBILITY AND PROCEEDED INBOUND TO THE RWY ON THE LOC. WHEN WE MADE THE DSCNT TO MDA; WE BASED OUR DSCNT ON THE CARLETON VOR; BUT FAILED TO REALIZE THE LOCATION OF CARLETON WITH RELATION TO THE ARPT; DUE TO THE 'RUSH' ATMOSPHERE OF THE CHANGING OF RWYS. UPON REALIZING OUR MISTAKE; WE WERE IN THE CLR AND PROCEEDING ON THE LOC TO THE RWY. THE CAPT AND I BOTH HAD KNOWN IF WE WENT IMC WE WOULD INITIATE THE GAR. BUT WE WERE IN GOOD VISIBILITY CONDITIONS AND PROCEEDED INBOUND AND LANDED WITH NO PROB. BASICALLY; WHAT WE DID WAS A CONTACT APCH; AND AT NO TIME WAS THE ACFT PUT IN AN UNSAFE POS.