What time that elapsed since noon is equal to half the time that remains until midnight?

Let the time that has elapsed since noon be ( x ) hours. The time remaining until midnight is ( 12 - x ) hours. According to the problem, ( x = \frac{1}{2}(12 - x) ). Solving this equation gives ( x = 4 ). Therefore, 4 hours after noon (which is 4 PM) is equal to half the time remaining until midnight.