ACR LTT PIC TAXIES TOWARDS WRONG RWY. AND TOO RAPIDLY.

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WE REQUESTED CLRNC FROM GND CTL TO TAXI TO THE ACTIVE RWY WITH THE CURRENT ATIS INFO. WE WERE CLRED TO TAXI FROM OUR ASSIGNED GATE TO THE ACTIVE RWY 31R AS ANNOUNCED ON THE CURRENT ATIS. THE CAPT BEGAN TAXIING AS INSTRUCTED; AND I; THE FO; BEGAN TO READ THE TAXI CHKLIST ITEMS. IN BTWN ITEMS; I LOOKED OUTSIDE THE ACFT AND; AT 1 POINT; NOTICED THE CAPT HAD MADE A WRONG TURN AND CROSSED A NON- ACTIVE RWY ENRTE TO 13L NOT 31R. I BROUGHT IT TO THE CAPT'S ATTN AND DSM GND ADVISED US THAT HE CLRED US TO RWY 31R NOT 13L AND CLRED US FROM OUR PRESENT POS; A 180 DEG TURN AND TAXI TO 31R. THE CAPT REVIEWED THE CURRENT WIND CONDITIONS WHICH WERE A 90 DEG XWIND TO EITHER RWY. HE INSTRUCTED ME TO REQUEST CLRNC TO 13L. WE WERE THEN CLRED TO TAXI FROM PRESENT POS TO 13L AND DID SO WITHOUT INCIDENT. CONTRIBUTING FACTORS TO THE MISHAP WERE THE CAPT'S LOSS OF SITUATIONAL AWARENESS. HE THOUGHT WE WERE SUPPOSED TO TAXI TO 13L NOT 31R. I ALSO FEEL HIS TAXI SPD IS EXCESSIVE AND I HAVE TOLD HIM SO IN THE PAST. I ALSO FEEL MY INADEQUATE DIVISION OF ATTN WAS A FACTOR. I HAD MY HEAD DOWN READING THE TAXI CHKLIST AND WAS NOT LOOKING OUTSIDE THE ACFT WHEN THE CAPT MADE THE WRONG TURN. I ALSO THINK WE WERE BOTH A LITTLE FATIGUED AFTER FLYING A LONG WKEND IN IFR CONDITIONS.