Consider a regular 12 hour clock, and measure time in hours starting from noon. Let denote the angle that the minute hand makes with the top position (12). Similarly, let be the angle that the hour hand makes with the vertical position. In this case, suppose we measure the angle clockwise, so that the angles involved are positive.
At 2:30pm we have
degrees.
At that time the minute hand has completed two and half rotations, and so the angle
degrees. (Enter a number between 720 and 1080.)
In general, at time
degrees, and
degrees.
There is a time between and pm at which the minute hand is on top of the hour hand. At that time the hour hand forms an angle of degrees with the vertical.
Hint: Set up and solve an equation for the time where the two hands point in the same direction, and then multiply the time with 30 to get the required angle.

You can earn partial credit on this problem.