Question

An accurate clock shows 9 a.m. Through how many degrees will the hour hand rotate when the clock shows 7 p.m.?

• A. 120°
• B. 300°
• C. 180°
• D. 210°

Hint:

Remember the speeds of clock hands: the hour hand moves at 0.5° per minute (30° per hour), and the minute hand moves at 6° per minute (360° per hour).

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
We need to calculate the total angle of rotation of the hour hand of a clock between 9 a.m. and 7 p.m. on the same day.
Step 2: Key Formula or Approach:
The hour hand of a clock completes a full 360° rotation in 12 hours. We can use this to find the rate of rotation per hour.
Rate of hour hand rotation = \(\frac{360^\circ}{12 \text{ hours}} = 30^\circ \text{ per hour}\).
Total angle = (Total hours elapsed) \(\times\) (Rate of rotation per hour).
Step 3: Detailed Explanation:
First, we calculate the total time elapsed from 9 a.m. to 7 p.m.
From 9 a.m. to 12 p.m. (noon) = 3 hours.
From 12 p.m. (noon) to 7 p.m. = 7 hours.
Total hours elapsed = 3 + 7 = 10 hours.
Next, we calculate the total angle rotated by the hour hand in these 10 hours.
\[ \text{Total Angle} = 10 \text{ hours} \times 30^\circ/\text{hour} \] \[ \text{Total Angle} = 300^\circ \] Step 4: Final Answer:
The hour hand will rotate through 300 degrees from 9 a.m. to 7 p.m.