Question

What is the measure of the angle of the hands on a clock if it is 3:24?

Answer 1

42deg

Explanation:

Let's see.

We'll consider 12:00 the "starting position"

The minute hand moves with the speed of 360deg in an hour, so 6deg per minute.

The hour hand moves with the speed of 360deg in 12hours, so 30deg per hour, so 0.5deg per minute.

at 3:24, the minute hand has moved 24*6deg=144deg from the starting position, while the hour hand has moved by 3*30deg + 24*0.5deg = 102deg

The absolute difference of the angles is 144deg-102deg = 42deg and it's the angle between the hands.

Answer 2

from 3 o’clock until 3:20, the minute hand will move 1/3 of the way around the circle or 120 degrees. But the hour hand has also moved 1/3 of the way to the next number, or 10 degrees.