10 minute, and the sum of two people's journeys is 600 * (3+2) = 3000m.

3000 divided by 90=33 is greater than 30, so they swam together 33 times.

If you start from both ends, the first encounter needs 1 the whole journey.

The second meeting went through three complete journeys together.

We met for the third time and left for five times.

Meet for the nth time, take 2n- 1.

2n- 1=33 n= 17

So we walked 33 times and met 17 times.

However, this algorithm can only calculate the number of head-on confrontations. If you want to calculate both frontal encounter and chase and encounter, you'd better draw a Liuka diagram (similar to the principle of a linear function image). The period you mentioned in your analysis refers to the period of drawing six cartoons.

The drawing method is as follows: Ask A to walk the whole journey alone, and B to walk the whole journey alone. A is 90 divided by 3=30 seconds.

B is 90 divided by 2 45 seconds, and then draw two parallel lines, the distance between the lines indicates the distance between the two places, and the horizontal direction indicates the time. Then mark the time points and connect them respectively. A uses a solid line and b uses a dotted line. Then the intersection of real and imaginary points is an encounter. And when A returns to the starting point at a certain point, B also returns to the starting point, even if it is a cycle. This period can be calculated and should be twice the least common multiple of their time, that is, 180 seconds. However, some people regard the least common multiple of 90 seconds as a period, which is inaccurate, because 90 seconds is only the middle point of the period, and the image is only about 90 seconds symmetrical.

Having said that, there is not a picture I can't express. Find a teacher and ask him to tell you something about Liukatu, or search online yourself.