Option C: 65
To solve this problem, we need to determine when the hour and minute hands of the clock will be aligned one above the other after initially being aligned between 8 o'clock and 9 o'clock.
  ● Step 1: Calculate the initial position of the hour and minute hands at 8 o'clock.  
        ○ At 8:00, the hour hand is at 240 degrees (since each hour represents 30 degrees, and 8 hours is \(8 \times 30 = 240\) degrees).
        ○ The minute hand is at 0 degrees.
  ● Step 2: Determine the rate of movement for each hand.  
        ○ The minute hand moves at 6 degrees per minute (since it completes 360 degrees in 60 minutes).
        ○ The hour hand moves at 0.5 degrees per minute (since it completes 30 degrees in 60 minutes).
  ● Step 3: Set up the equation for when the hands are aligned.  
        ○ Let \( t \) be the time in minutes after 8:00 when the hands are aligned.
        ○ The position of the minute hand after \( t \) minutes is \( 6t \) degrees.
        ○ The position of the hour hand after \( t \) minutes is \( 240 + 0.5t \) degrees.
  ● Step 4: Solve for \( t \) when the hands are aligned.  
        ○ The hands are aligned when their positions are equal:
      \[
      6t = 240 + 0.5t
      \]
        ○ Simplify the equation:
      \[
      6t - 0.5t = 240
      \]
      \[
      5.5t = 240
      \]
        ○ Solve for \( t \):
      \[
      t = \frac{240}{5.5} \approx 43.64
      \]
  ● Step 5: Calculate the next alignment after the initial one.  
        ○ The hands align every 360 degrees relative to each other.
        ○ The relative speed of the minute hand compared to the hour hand is \( 6 - 0.5 = 5.5 \) degrees per minute.
        ○ Time for the next alignment after the initial one:
      \[
      \frac{360}{5.5} \approx 65.45
      \]
  ● Step 6: Round to the nearest integer.  
        ○ The nearest integer to 65.45 is 65.
 Therefore, the two hands will be aligned again approximately 65 minutes after the initial alignment.