This is actually the encounter problem that we usually solve. Let's first find out the angle at which the hour hand and the minute hand walk every minute, and then calculate the time when the two hands form a 90-degree angle.

First of all: the hour hand goes 30 degrees an hour, which means it goes 0.5 degrees a minute.

The minute hand moves every minute (360/60=6), which is 6 degrees.

We began to calculate, and after a few minutes, the hour hand and the minute hand made an angle of 90 degrees. At 6 o'clock sharp, the difference between the minute hand and the hour hand is 180 degrees, which can be regarded as the minute hand chasing the hour hand. Suppose the minute hand and the hour hand make an angle of 90 degrees in x minutes. The following equation is obtained:

( 180-6X)+0.5X=90

(180-6X) means that when the minute hand and the hour hand are at 90 degrees, the angle between the minute hand and the hour hand is the key, so we should understand it well.

0.5X is the angle taken by the hour hand when the minute hand and the hour hand form 90 degrees.

Then solve the above equation to get x =180/11(16 and 4/1/min).

After about 16 minutes and 2 1.8 seconds, the hour hand and the minute hand form a 90-degree angle, that is, 2 1 second after 6: 00.

The above is the time required for the minute hand not to exceed the hour hand.

Next, calculate that the minute hand becomes 90 degrees again after passing the hour hand. The method is as above. Of course, here we can simply think that. After the two needles met, the minute hand and the hour hand became 90 degrees again. But the question you gave is to know when the two needles become 90 degrees. Even calculating the time when two needles meet and become 90 degrees, it is troublesome to know the time when two needles meet and the time when they become 90 degrees.

Why not start counting at 6: 30? When the minute hand is catching up with the hour hand, the included angle between the minute hand and the hour hand is 15 degrees. (Why 15 degrees, because the hour hand left 15 degrees for half an hour, and the minute hand is just on the word 6.) Assuming that the two hands are 90 degrees after x minutes, the equation is obtained:

6X- 15-0.5X=90, where 6X is the angle taken by the total * * * from 6: 30 to the intersection of two pins. Subtract the extra angle between the start and the hour hand, and then subtract the hour hand angle of x minutes.

The final release is X= 150/ 1 1 min (approximately equal to 13 minutes and 38 seconds).

That is, from 6: 30, plus150/1min, that is, about 6: 43: 38, the hour hand and the minute hand form a 90-degree angle.

Of course, the above are just the specific ideas and processes to solve the problem. To get the answer quickly, it is better to turn the minute hand directly to see the specific time, minute and second, and the minute hand forms a 90-degree angle with the hour hand. But in order to get accurate figures, calculations must be made, just to get an approximate time.