Question: how long does it take for the moon to move from new moon to first quarter?
Answer: So quarter of this period of 28 days, needed to change from new moon to 1st quarter, equals at least 28/4 = 7 days. Most months (moons) however last a bit longer than 28 days, even up to 31 days, so at layman level the answer lies between 28/4 = 7 days and 31/4 = 7.75 days.