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.?

the ratio of the distance in inches travelled by the tip of the hour hand to the distance in inches travelled by the tip of the minute hand is 0.125.

Step-by-step explanation:

The given information is:

length of the hour hand, l = 6 inches length of the minute hand, b = 8 inches

Therefore, since the tip of the minute moves from 12 to 3, it moved a distance of:

s₁ = r θ

s₁ = (8) (π/2)

s₁ = 4π inches

The hour hand moves 30 degrees / 60 = 1/2 degree in a minute.

Therefore, in 30 minutes the hour hand moves a distance of:

s₂ = r θ

s₂ = 6 (30*1/2*π/180)

s₂ = π/2 inches

Therefore, the ratio of the distance in inches travelled by the tip of the hour hand to the distance in inches travelled by the tip of the minute hand is:

s₂ / s₁ = (π/2) / 4π

s₂ / s₁ = 0.125