Question

Neela’s clock is broken. The minute hand rotates around the clock correctly, but the hour hand is stuck in the three o’clock position. Suppose Neela first looks at the clock when the hands are aligned and it shows 3:15. She looks at the clock again and sees that the hour and minute hands of the clock form the arms of an angle measuring −105°. How many degrees could the minute hand have rotated to reach its current position? (1 point)

Responses
−465°
−375°
−435°
−95°

Answer 1

[AI-generated answer — Bot GPT 3.5]

−435°

To solve this problem, we need to determine the initial angle between the hour and minute hands when Neela first looked at the clock and the angle between them when she looked at the clock again.

1) When the clock showed 3:15, the hour hand was at the 3 position and the minute hand was at the 3 position. The minute hand had traveled 75 degrees past the 12 position (15 minutes * 6 degrees per minute = 90 degrees), making an angle of 75 degrees with the hour hand.

2) When the angle between the hour and minute hands was -105 degrees, the hour hand would be at the 3 position and the minute hand would have traveled an additional 45 degrees beyond its position at 3:15 (105 degrees - 75 degrees = 30 degrees).

Therefore, the minute hand has rotated a total of 75 + 45 = 120 degrees beyond the 3:15 position. Since the minute hand moves at a rate of 6 degrees per minute, it could have rotated in total -420 degrees to reach its current position.

So, the answer is -420 degrees, but the closest option provided is -435 degrees.