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 hand of the clock form the angle measuring -105 degrees. How many degrees could the minute hand have rotated to reach its current position?

Question

show all your work
A -465
B -375
C-435
D-95

Answer 1

To find the number of degrees the minute hand has rotated, we first need to determine the position of the minute hand when the clock showed 3:15.

At 3:15, the minute hand is pointing at the 3-minute mark, while the hour hand is pointing between the 3 and 4-hour marks. The minute hand is 90 degrees behind the hour hand every hour, so for 15 minutes, it would be 90/4 = 22.5 degrees behind the hour hand. Therefore, the minute hand at 3:15 is at an angle of 90 + 22.5 = 112.5 degrees from the vertical 12 o'clock position.

Now, since at the current position, the hands form an angle of -105 degrees, we can calculate the angle between the hands as follows:

Angle between the hands = 112.5 - 105 = 7.5 degrees

The minute hand could have gone from its initial position at 3:15 to its current position by moving 7.5 degrees. Therefore, the minute hand has moved 7.5 degrees to reach its current position.

So, the correct answer is:

D - 95