Math clock face problems, math problems on the clock face to find practices and answers

All four of these questions can be boiled down to the problem of catching up with the hour and minute hands.

The minute hand travels 6° in one minute, and the hour hand moves in one minute.

1.At 3 o'clock, the angle between the two needles is 90°. After 90 minutes (the first coincidence.)

2.At 5 o'clock, the angle between the two needles is 150°. After 150 minutes (minutes coincide.

3.At 7 o'clock, the distance to be reached by the minute hand is 210°. After 210 minutes, i.e. at 7 o'clock the two hands coincide.

4.At 6 o'clock, the angle between the two needles is 180°. After 180 (minutes coincide.

The week is 360, the minute hand moves 6 minutes a minute, and the hour hand moves a minute and coincides after x minutes;

1.x=900 59 approx.

2.x=1500 59 approx.

3.x=2100 59 is about at 7 o'clock.

4.x=1800 59 approx.

It takes 720 minutes for the hour hand to rotate one week, so every minute it turns.

It takes 60 minutes for the minute hand to turn one week, so it turns 6 degrees per minute.

The minute hand rotates more than the hour hand per minute.

Because of the triumph of the three strokes, the time is between hours and 2 hours, so the multi-rotation degree of the minute hand is between 495 and 660 degrees.

Therefore, when the two hands are again in the same straight line, the minute hand can only rotate more than the hour hand (540 degrees of digging button).

Therefore, the elapsed time is 540 minutes.

In less than 1 hour, it means that the minute hand is in front of the hour hand, indicating that the hour hand + minute hand has gone in a circle.

t/12+t=60

1.Solution: Between 6 o'clock and 7 o'clock on the clock face, the hour hand and minute hand coincide at 6 o'clock x minute, the hour hand travels in degrees per minute, and the minute hand travels 6 degrees per minute; According to the title, it gets:

Solution, get: x=32 and 8 11

The coincidences of the instant and minute hands at 6:32 and 8:11.

2.Solution: The hour hand travels degrees per minute, the minute hand travels 6 degrees per minute, and when the minute hand and the hour hand are exactly in a straight line between 7 o'clock and 8 o'clock, they are set at 7 o'clock x minutes

Solution, get: x = 5 and 5 11 minutes, between 7 o'clock and 8 o'clock when the minute hand and the hour hand coincide, set at 7 o'clock y minutes, according to the title, get:

Solution, get: y = 38 and 2 11 minutes.

That is, Xiao Ming spent 32 and 8 11 minutes to solve the problem.