How many minutes past 5:13 will the hands of an analog clock next be 12 degrees apart?
To determine the number of minutes past 5:13 when the hands of an analog clock are 12 degrees apart, we need to understand the relationship between the hands of a clock and their movement.
On an analog clock, the minute hand moves 360 degrees in 60 minutes, which means it moves 6 degrees per minute (360/60 = 6). Similarly, the hour hand moves 360 degrees in 12 hours, which means it moves 30 degrees per hour (360/12 = 30) or 0.5 degrees per minute (30/60 = 0.5).
Now, to calculate when the hands of the clock will be 12 degrees apart, we can set up the following equation:
6x - 0.5x = 12
Here, 'x' represents the number of minutes past 5:13.
Simplifying the equation, we have:
5.5x = 12
To solve for 'x', divide both sides of the equation by 5.5:
x = 12 / 5.5
Using a calculator, we find:
x ≈ 2.182
So, the number of minutes past 5:13 when the hands of the analog clock will next be 12 degrees apart is approximately 2.182 minutes.