What degrees of the smaller angle made with the long hand and an hour hand at 7:18?
When a clock advances from seven o’clock, the long hand will run after the hour hand.
Because the long hand goes ahead 360° for one hour (60 minutes), it goes ahead 360°/60 = 6 degrees in one minute.
Because the hour hand goes ahead one clock face = 30 degrees for one hour, it goes ahead 30°/60 = 0.5 degrees in one minute.
When the long hand runs after the hour hand, the angle between the both hands is shortened by 6° - 0.5° = 5.5 degrees in one minute.
The angle of both needles is shortened by 5.5° × 18 ＝ 99 degrees for 18 minutes until 7:18.
Since the difference at 7:00 was 210 degrees, the degrees of angle st 7:18 is 210° - 99° = 111 degrees.
Answer
111 degrees
Solution
An angle of the long hand and the hour hand is 30° × 7 = 210 degrees at 7:00.
When a clock advances from seven o’clock, the long hand will run after the hour hand.
Because the long hand goes ahead 360° for one hour (60 minutes), it goes ahead 360°/60 = 6 degrees in one minute.
Because the hour hand goes ahead one clock face = 30 degrees for one hour, it goes ahead 30°/60 = 0.5 degrees in one minute.
When the long hand runs after the hour hand, the angle between the both hands is shortened by 6° - 0.5° = 5.5 degrees in one minute.
The angle of both needles is shortened by 5.5° × 18 ＝ 99 degrees for 18 minutes until 7:18.
Since the difference at 7:00 was 210 degrees, the degrees of angle st 7:18 is 210° - 99° = 111 degrees.
