between 3 p.m. and 3:30 P.M., the minute hand of a clock moves 180. How many degrees does the hour hand move during that same period of time
in 12 hours the hour hand moves 360°
so in 1 hour it moves 360/12 or 30°
so in 1/2 hour it would move ...... °
To determine the number of degrees the hour hand moves between 3 p.m. and 3:30 p.m., we need to understand the relationship between the hour hand and the minute hand on a clock.
A typical clock has 12 hours marked on its face, which corresponds to 360 degrees. Therefore, each hour mark represents 360/12 = 30 degrees.
In this case, we are interested in the time between 3 p.m. and 3:30 p.m., which corresponds to one half hour. As stated in the question, the minute hand moves 180 degrees in this period.
To calculate the degrees moved by the hour hand, we need to determine the fraction of the hour that has passed. Since we have half an hour (30 minutes) in this case, we divide it by the total number of minutes in an hour, which is 60. Therefore, the fraction of the hour that has passed is 30/60 = 1/2.
Now, we can calculate the degrees moved by the hour hand. Since the hour hand moves 30 degrees per hour and only half an hour has passed, the degrees moved by the hour hand is 30 * (1/2) = 15 degrees.
Hence, the hour hand moves 15 degrees during the period between 3 p.m. and 3:30 p.m.