The minute hand of the watch is three times longer than the second hand; how many times faster

The minute hand of the watch is three times longer than the second hand; how many times faster does the second hand move than the minute hand?

Rm = 3 * Rs.
Nm = 1.
Nc = 60.
Vs / Vm -?
For 1 revolution of the minute hand, the second hand makes 60 revolutions.
Vs = 2 * P * Rs / 60 s.
Vm = 2 * P * Rm / Nc * 60 s = 2 * P * 3 * Rc / Nc * 60 s.
Vs / Vm = 2 * P * Rs / 60 s: 2 * P * 3 * Rs / Ns * 60 s = Ns / 3.
Vs / Vm = 60/3 = 20.
Answer: the speed of the second hand is 20 times higher than the speed of the minute hand: Vc / Vm = 20.



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