Short Answer 
The hour and minute hands of a clock complete their revolutions at different rates, with the minute hand making a full revolution every 72 minutes and the hour hand every 720 minutes. By calculating their speeds and using the equation for alignment, it is determined that the hands will align again after 80 minutes.
Step 1: Understand the Movements of the Hands
The movements of the hour and minute hands are crucial for solving the alignment issue. The minute hand completes a full revolution every 72 minutes, while the hour hand goes through a full revolution every 12 hours or 720 minutes. This difference in timing affects how and when they align again.
Step 2: Determine Their Relative Speed
Next, we need to compare the speeds of both hands to find out when they will meet. The minute hand travels at a speed of 5 degrees per minute, calculated as 360 degrees/72 minutes. Conversely, the hour hand moves at a speed of 0.5 degrees per minute, computed as 360 degrees/720 minutes. Their relative speeds will help us know when they align.
Step 3: Determine When the Hands Align
To find out when the hands will align, we set up an equation based on their movements. The hands will match when the angle between them equals an integer multiple of 360 degrees. Using the equation 5t = 0.5t + 360n, where n is a full rotation count, we solve for t. The minimal positive t occurs when n = 1, leading to t = 80 minutes, meaning they will align again after 80 minutes.