B737-800 FLIGHT CREW DEPARTING DTW NOTICES AN AIRCRAFT ON FINAL AND DELAYS IN TAKING THE RUNWAY BECAUSE OF CONFLICTING TRAFFIC ON APPROACH TO THE SAME RUNWAY.

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WE WERE CLRED FOR TKOF ON RWY 4R AT DTW (CLRNC TO TKOF AND TURN TO A HDG OF 020 DEGS). AS WE STARTED TO ROLL TOWARD THE RWY; WE NOTICED AN ACR Y ACFT ON FINAL. THE FO QUESTIONED IF IT WAS COMING TO OUR RWY; SO WE STOPPED PRIOR TO TAKING THE RWY BUT AFTER XING THE ILS LINE; THE ACR Y CALLED TWR AND SAID 'WE ARE CLR TO LAND ON RWY 4R; RIGHT?' AFTER A LONG PAUSE; THE TWR DIRECTED ACR Y TO GO AROUND AND STATED 'I HAVE AN ALERT; GO AROUND; AND I DON'T KNOW WHY.' WE HELD SHORT OF THE THRESHOLD LINE AND INFORMED TWR THAT WE WERE NOW HOLDING SHORT. AFTER ACR Y HAD INITIATED ITS MISSED APCH; THE TWR SAID 'ACR X; YOU ARE CLRED FOR TKOF AGAIN; FLY HDG 020 DEGS.' THE THINGS THAT PREVENTED A SERIOUS ACCIDENT WERE THE FACT THAT BOTH ACFT CREWS WERE WATCHING AND QUESTIONING THE APPARENT CONFLICT OF CLRNCS. WE TOOK ACTION BY STOPPING SHORT OF THE RWY AND ACR Y TOOK ACTION BY GOING AROUND. SUPPLEMENTAL INFO FROM ACN 810081: I ASKED CAPT 'HEY; IS HE FOR THE LEFT?' I THEN HEARD AN ACR Y ACFT ASK TO CONFIRM LNDG CLRNC FOR RWY 4R. I YELLED OUT 'STOP! STOP!' IN THE COCKPIT. CAPT THEN BROUGHT THE ACFT TO AN ABRUPT HALT SHORT OF RWY 4R BUT PAST THE HOLD SHORT BARS. WE THEN PERFORMED A NORMAL TKOF WHILE ACR Y PERFORMED A MISSED APCH. TFC APPEARED LIGHT.