Strips. Tri-tip strips cook to rare in about 8 to 10 minutes, and to medium in 12 to 14 minutes. This is the total cooking time, so turn the strips over at the halfway point -- 4 to 5 minutes on each side for rare, and 6 to 7 minutes on each side for medium.Calman Lugo/iStock/Getty Images.trips. Tri-tip strips cook to rare in about 8 to 10 minutes, and to medium in 12 to 14 minutes. This is the total cooking time, so turn the strips over at the halfway point -- 4 to 5 minutes on each side for rare, and 6 to 7 minutes on each side for medium. Calman Lugo/iStock/Getty Images.