The minute hand of the clock is 3 times the hour hand. Find the ratio of linear velocities.

Given:
r2 = 3 * r1 – the minute hand of the clock is 3 times larger than the hour hand;
π = 3.14 – geometric constant (Pythagorean number);
t2 = 1 hour = 3600 seconds – the time during which the minute hand makes a full revolution;
t1 = 12 hours = 43200 seconds – the time during which the hour hand makes a full revolution.
It is required to determine v2 / v1 – the ratio of linear velocities.
The linear speed of the hour hand is:
v1 = c1 / t1 = 2 * π * r1 / t1 = 2 * π * r1 / 43200 = π * r1 / 21600.
The linear velocity of the minute hand is:
v2 = c2 / t2 = 2 * π * r2 / t2 = 2 * π * r2 / 3600 = π * r2 / 1800 = 3 * π * r1 / 1800 = π * r1 / 600.
Then:
v2 / v1 = (π * r1 / 600) / (π * r1 / 21600) = 21600/600 = 36.
Answer: The ratio of linear velocities is 36.