Current location - Training Enrollment Network - Mathematics courses - Huajinbei math problems
Huajinbei math problems
45+75 =120m/min

400/ 120= 10/3 minutes

When we first met, B moved 45 * 10/3 = 150m clockwise.

If we want to meet for the second time, the sum of the distances that Party A and Party B have to move is 400 meters, which is the same as when we first met.

So when we met for the second time, B moved the same 150m clockwise.

Then move on.

There are two ways to ask about the number of meetings on the CD.

Method 1: Direct dial number

When we first met, B moved 45 *10/3 =150m clockwise and met at the midpoint of BC.

At the second meeting, B moves clockwise again, and the same150m meets at point D..

At the third meeting, B moves clockwise again, and the same150m meets at the midpoint of AB.

Similarly, the fourth meeting was at point C.

The fifth meeting was held in the middle of AD.

The sixth meeting was at point B.

The seventh meeting is at the midpoint of the CD.

So this is our seventh meeting.

Method 2:

Let's assume that the x meeting

In order for two people to meet between CDs, the distance that B moves when meeting must be 150x.

200 & lt 150 x & lt; 300 or 600 <150 x <; 700 or1000 <150 x <; 1 100 .....

That is 200+400k K.

Then use two variables to solve this inequality, as long as x and k must be integers, they can be solved.

When the inequality is divided by 50 at the same time, 4+8k

Subtract 8k at the same time to get 4.

Because x and k are integers, 3x-8k should also be integers.

So 3x-8k can only get 5.

That is 3x-8k=5.

3x=8k+5

This is an indefinite equation. If you are going to take part in the China Competition, you should know its solution.

When k= 1, x= 13/3, which does not meet the requirements.

When k=2, x=2 1/3=7.

So the smallest integer solution of x is 7.

Therefore, the first meeting on the edge of the CD should be the seventh meeting.