A clock works only for 16 out of 24 hours every day. But in those 16 hours, it moves at a uniform rate and shows the passing of 24 hours. Another clock works only for 12 hours out of every 24 hours. If it moves at twice the speed of the first clock, how many days does it take to display the passing of 9 days?
Question
A clock works only for 16 out of 24 hours every day. But in those 16 hours, it moves at a uniform rate and shows the passing of 24 hours. Another clock works only for 12 hours out of every 24 hours. If it moves at twice the speed of the first clock, how many days does it take to display the passing of 9 days?
Solution
Sure, let's break it down:
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The first clock works for 16 hours but shows the passing of 24 hours. This means that for every 2/3 of an hour (16/24), it shows the passing of 1 hour.
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The second clock works for 12 hours but moves at twice the speed of the first clock. This means that for every 1/3 of an hour (2/3 divided by 2), it shows the passing of 1 hour.
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Therefore, in 12 hours, the second clock shows the passing of 36 hours (12 divided by 1/3).
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To display the passing of 9 days (or 216 hours), the second clock would need to work for 72 hours (216 divided by 3).
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Since the second clock only works for 12 hours out of every 24 hours, it would take 6 days for it to work for 72 hours (72 divided by 12).
So, it would take the second clock 6 days to display the passing of 9 days.
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