I looked at the clock when I went out of the house, the long hand pointed between 5:35 and 5:40.
When I came home within two hours, the position of the long hand and the hour hand was just replaced from the position when I went out.
What time was it when I came home ?
When I came home within two hours, the position of the long hand and the hour hand was just replaced from the position when I went out.
What time was it when I came home ?
Answer
The ratio of the angle the long hand to the hour hand turning around is 6 degrees : 0.5 degrees = 12 : 1.
The angle that an hour hand surrounded is calculated by the proportional distribution of 720 degrees × 1/(1 + 12)= 720/13°.
The differences degrees of the angle between long hand and the hour hand at the time of 7:00 are 30 degrees × 7 = 210°.
When I came home, the difference was shortened to 210° - 720/13° = 2010/13°.
The time to be taken to shorten by 2010/13° is 2010/13°/ (6° - 0.5°) = 4020/143 minutes.
7 o'clock and 4020/143 minutes
Solution
The sum of angle that the long hand and an hour hand turned around during going out is 720 degrees.
The ratio of the angle the long hand to the hour hand turning around is 6 degrees : 0.5 degrees = 12 : 1.
The angle that an hour hand surrounded is calculated by the proportional distribution of 720 degrees × 1/(1 + 12)= 720/13°.
The differences degrees of the angle between long hand and the hour hand at the time of 7:00 are 30 degrees × 7 = 210°.
When I came home, the difference was shortened to 210° - 720/13° = 2010/13°.
The time to be taken to shorten by 2010/13° is 2010/13°/ (6° - 0.5°) = 4020/143 minutes.
