The hour hand of a clock is 6 inches long and the minute hand is 8 inches long. What is the ratio of the distance in inches traveled by the tip of the hour hand to the distance in inches traveled by the tip of the minute hand from noon to 3 p.m.? Express your answer as a common fraction.
+592 the hour hand traveled 1/4 of the circumference of the circle with 6 inches as a radius, which is 12$\pi$/4=3$\pi$, where the minute hand traveled the whole circumference of the circle with radius 8 inches 3 times, which is 16$\pi\cdot$3=48$\pi$
so the ratio is 3$\pi$:48$\pi$, and simplified: $\boxed{1:16}$
+592 the hour hand traveled 1/4 of the circumference of the circle with 6 inches as a radius, which is 12$\pi$/4=3$\pi$, where the minute hand traveled the whole circumference of the circle with radius 8 inches 3 times, which is 16$\pi\cdot$3=48$\pi$
so the ratio is 3$\pi$:48$\pi$, and simplified: $\boxed{1:16}$
