When Taro went out a house in the evening, he saw the clock and the long hand pointed between 5:35 and 5:40.
Taro came back within 2 hours and saw the clock.
The position of the long hand and the hour hand was reverse exactly comparing to the position when he went out.
Answer the following questions.
(1) Find the sum total of the angle which the long hand and the hour hand turned around during going out.
(2) Find the angle which the hour hand turned around during going out.
(3) Find the time when he returned home.
Answer
(1) 720 degrees
(2) 720/13 degrees
(3) 7 o’clock and 4020/143 minutes
Solution
(1) The figure shows the time Taro went out and the right figure shows time he came home.
This figure shows that the time he came home is 7:25 ~ 7:30.
While he was out of home, the long hand turned around by the angle of two round (360° × 2 = 720°） minus A degrees.
The hour hand turned around by A degrees.
The sum total of the angle around which both of hands turned is (720 degrees - A degrees) + A degrees = 720 degrees.
(2) The long hand moves 360 degrees in one hour and the hour hand moves 30 degrees in one hour.
The ratio of the angle each hand moves is 360 : 30 = 12 : 1.
The angle which the hour hand moved among 720 degrees is 720 × 1/(12+1) = 720/13 degrees.
(3) At 7:00, the angle of both hands is 30 degrees × 7 = 210 degrees.
At the time he returned, the difference is shortened by 210 - 720/13 = 2010/13 degrees.
The angle difference is shortened by 6 - 0.5 = 5.5 degrees per minute.
The time for shortening by 2010/13 degrees is 2010/13 / (6 - 0.5) = 4020/143 minutes.
The time he came home is 7 : 4020/143.
Taro came back within 2 hours and saw the clock.
The position of the long hand and the hour hand was reverse exactly comparing to the position when he went out.
Answer the following questions.
(1) Find the sum total of the angle which the long hand and the hour hand turned around during going out.
(2) Find the angle which the hour hand turned around during going out.
(3) Find the time when he returned home.
Answer
(1) 720 degrees
(2) 720/13 degrees
(3) 7 o’clock and 4020/143 minutes
Solution
(1) The figure shows the time Taro went out and the right figure shows time he came home.
This figure shows that the time he came home is 7:25 ~ 7:30.
While he was out of home, the long hand turned around by the angle of two round (360° × 2 = 720°） minus A degrees.
The hour hand turned around by A degrees.
The sum total of the angle around which both of hands turned is (720 degrees - A degrees) + A degrees = 720 degrees.
(2) The long hand moves 360 degrees in one hour and the hour hand moves 30 degrees in one hour.
The ratio of the angle each hand moves is 360 : 30 = 12 : 1.
The angle which the hour hand moved among 720 degrees is 720 × 1/(12+1) = 720/13 degrees.
(3) At 7:00, the angle of both hands is 30 degrees × 7 = 210 degrees.
At the time he returned, the difference is shortened by 210 - 720/13 = 2010/13 degrees.
The angle difference is shortened by 6 - 0.5 = 5.5 degrees per minute.
The time for shortening by 2010/13 degrees is 2010/13 / (6 - 0.5) = 4020/143 minutes.
The time he came home is 7 : 4020/143.
