The analog clock shown has a minute hand with an arrow tip that is exactly twice as far from the clock\u2019s center as the hour hand\u2019s arrow tip. If point A is at the tip of the minute hand, and point B is at the tip of the hour hand, what is the ratio of the distance that point B travels in 3 hours to the distance that point A travels in 9 hours? Express your answer as a common fraction.