The clock has been set at the correct time at 12 noon. Current time is 4:10:00 PM. How many degrees has the hour hand turned through?
Question
The clock has been set at the correct time at 12 noon. Current time is 4:10:00 PM.
How many degrees has the hour hand turned through?
Solution
To calculate the degrees the hour hand has turned through, we need to understand that the hour hand moves 360 degrees in 12 hours (or 30 degrees per hour).
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First, calculate the time elapsed since 12 noon. The current time is 4:10 PM, so 4 hours and 10 minutes have passed.
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Next, calculate the degrees turned in the full hours that have passed. 4 hours * 30 degrees/hour = 120 degrees.
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Then, calculate the additional degrees turned in the 10 minutes that have passed. Since the hour hand moves 0.5 degrees per minute (30 degrees per hour / 60 minutes), it has moved an additional 5 degrees in the 10 minutes.
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Finally, add the degrees turned in the full hours to the degrees turned in the minutes. 120 degrees + 5 degrees = 125 degrees.
So, the hour hand has turned through 125 degrees since 12 noon.
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