Answer :
Final answer:
The hour and minute hands of a grandfather clock at 8:00 am will first meet approximately 44 minutes later, which is not an option provided among a) 10 minutes, b) 20 minutes, c) 30 minutes, or d) 40 minutes.
Explanation:
To find out when the hour and minute hands of a grandfather clock will first meet after 8:00 am, we can use a little bit of math. The minute hand moves 360 degrees in 60 minutes, while the hour hand moves 360 degrees in 12 hours (or 720 minutes). This means the minute hand moves 6 degrees per minute, and the hour hand moves 0.5 degrees per minute.
At 8:00 am, the hour hand is exactly at the 8-hour mark, and the minute hand is at 12, which is a 240-degree separation (as 8 hours × 30 degrees per hour = 240 degrees). The hands will meet when their positions coincide, so we need to figure out when the minute hand will catch up to that 240-degree lead the hour hand has.
Let x represent the number of minutes past 8:00 am. In x minutes, the minute hand will travel 6x degrees, and the hour hand will travel 240 + 0.5x degrees. They meet when 6x = 240 + 0.5x, which simplifies to 5.5x = 240. Dividing both sides by 5.5, we find x = 240 / 5.5, which is approximately 43.64 minutes.
Therefore, the closest whole number answer is actually not in the options given as the hands first meet approximately 44 minutes past 8:00 am, not within the answer choices provided of a) 10 minutes, b) 20 minutes, c) 30 minutes, or d) 40 minutes.
