How many hours does it take for the hour hand to travel as far as the minute hand travels in 40 minutes?
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To determine how many hours it takes for the hour hand to travel as far as the minute hand travels in 40 minutes, we first need to understand the relative speeds of the hour and minute hands.
The hour hand completes a full revolution in 12 hours, while the minute hand completes a full revolution in 60 minutes (or 1 hour). This means that the hour hand travels 12 times slower than the minute hand in terms of revolutions per hour.
Since the minute hand completes a full revolution in 60 minutes, it means that in 40 minutes, the minute hand will have traveled 40/60 = 2/3 of a full revolution.
Now, to find out how many hours it takes for the hour hand to travel the same distance as the minute hand in 40 minutes, we divide the time it takes for the minute hand to travel by its relative speed compared to the hour hand.
Since the hour hand is 12 times slower than the minute hand, we divide 2/3 of a full revolution by 12 to find the equivalent fraction in hours.
(2/3) / 12 = 2/36 = 1/18
Therefore, it takes the hour hand 1/18 of an hour to travel the same distance as the minute hand travels in 40 minutes. To convert this into minutes, we multiply 1/18 by 60 (since there are 60 minutes in an hour):
(1/18) * 60 = 3.33 (rounded to two decimal places)
So, it takes the hour hand approximately 3.33 minutes to travel the same distance as the minute hand travels in 40 minutes.