Example 7 As shown in Figure 5, the perimeter of square $ABCD$ is $40 \mathrm{~m}$, two people, Jia and Yi, start from $A$ and $B$ respectively at the same time, and walk along the edges of the square. Jia walks counterclockwise at a speed of $35 \mathrm{~m}$ per minute, and Yi walks clockwise at a speed of $30 \mathrm{~m}$ per minute. If the notation $(a, b)$ represents that the two people have been walking for $a \mathrm{~min}$ and have met $b$ times, then, when the two people are at the two opposite vertices of the square for the first time after starting, the corresponding notation should be ( ).

保留源文本的换行和格式，直接输出翻译结果。
Explanation: After departure, every 2 minutes, both individuals arrive at a vertex simultaneously, with their respective positions as follows:
Time $(\mathrm{min}) \quad 0 \quad 2 \quad 4 \quad 6 \quad \cdots$
Position of A $\quad A \rightarrow D \rightarrow C \rightarrow B \quad \cdots$
Position of B $\quad B \rightarrow D \rightarrow B \rightarrow D \quad \cdots$
Therefore, $a=6$.
The first meeting occurs when the total distance traveled by both is $10 \mathrm{~m}$ (on edge $A B$), and thereafter, they meet again every time the total distance traveled reaches $40 \mathrm{~m}$. In $6 \mathrm{~min}$, the total distance traveled by both is $390 \mathrm{~m}$, so the number of meetings is
$$
1+\left[\frac{390-10}{40}\right]=1+9=10 \text {. }
$$

Therefore, $b=10$, the notation is $(6,10)$.
Note: Since the problem requires only the first "encounter," a tabular method can also be used.