Troopers say 22-year-old Brittany Bibbs was speeding on New Circle Road when they pulled her over.
State Police say during the stop, a passenger named Marquis Cottrell got out of the car and ran off.
Troopers say they caught Cottrell and arrested him on several charges including public intoxication, resisting arrest and possession of marijuana.
State Police say they searched the car and found a 9mm handgun and 253 grams of cocaine.
According to troopers, the cocaine is worth about $30,000.
Bibbs was also arrested and is being held at the Fayette County Detention Center.