Question 360054: A clock is broken. But its hour hand, minute hand, and second hand still move
at constant speeds in the normal direction. The second hand passes the hour hand
every 10 seconds (measured by an accurate clock) and passes the minute hand every
20 seconds. How often does the minute hand pass the hour hand?
Answer by Edwin McCravy(20056)   (Show Source):
You can put this solution on YOUR website! A clock is broken. But its hour hand, minute hand, and second hand still move
at constant speeds in the normal direction. The second hand passes the hour hand
every 10 seconds (measured by an accurate clock) and passes the minute hand every 20 seconds. How often does the minute hand pass the hour hand?
Imagine yourself holding the clock in your hands and constantly turning the
whole clock in the counterclockwise direction at the same speed the second hand
is turning, so that the second hand doesn't move at all, but stays in the same
place.
Now imagining that situation (with the second hand not moving at all), the hour
hand makes one revolution every 10 seconds. Therefore the hour hand's rate is
360 degrees per 10 seconds or 36 degrees per second.
Still imagining that situation (with the second hand not moving at all), the
minute hand makes one revolution every 20 seconds. Therefore the minute hand's
rate is 360 degrees per 20 seconds or 18 degrees per second.
So the angle between the hour and minute hands grows at the rate of 36-18 or 18
degrees per second, and since 18 degrees per second is the same as 360 degrees
per 20 seconds, then the angle between the hour and minute hands grows at the
rate of 360 degrees per 20 seconds. Therefore they pass each other every 20
seconds.
Edwin
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