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Answer :
Final answer:
The hour and minute hands of the clock will first meet approximately 44 minutes after 8:00 am, but this is not one of the provided answer choices.
Explanation:
To determine when the hour and minute hands of the clock will first meet after 8:00 am, we can use a simple calculation. At 8:00 am, the hour hand is exactly at the 8 and the minute hand is at the 12. Each hour on the clock represents 30 degrees, so the hour hand is 240 degrees (8×30) from the 12.
Now, the hour hand moves 0.5 degrees per minute (since it moves 30 degrees every hour and there are 60 minutes in an hour), while the minute hand moves at 6 degrees per minute (360 degrees for a full rotation divided by 60 minutes).
The minute hand needs to catch up to the hour hand. Since the hour hand is also moving, we must account for both their speeds. The catching up speed is 6 degrees (minute hand) - 0.5 degrees (hour hand) = 5.5 degrees per minute.
To find the number of minutes it takes for the minute hand to catch up 240 degrees, we use the formula:
Minutes = Degrees to catch up ÷ Catch up speed = 240 degrees ÷ 5.5 degrees per minute ≈ 43.64 minutes.
Therefore, the hands will first meet approximately 44 minutes after 8:00 am, which is not one of the provided answers. It's important to note that the actual time might be slightly different due to the discrete nature of the choices provided.
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