20. (6 points) Person A and Person B start from locations $A$ and $B$ respectively at the same time, heading towards each other. The speed ratio of A to B is 4:5. After they meet, if A's speed decreases by 25%, and B's speed increases by 20%, and they continue to travel in their original directions, when B reaches location $A$, A is 30 km away from location $B$. Therefore, the distance between $A$ and $B$ is $\qquad$ km.
20. (6 points) Person A and Person B start from points $A$ and $B$ respectively at the same time, heading towards each other. The speed ratio of A to B is $4: 5$. After they meet, if A's speed decreases by $25\%$ and B's speed increases by $20\%$, they continue to travel in their original directions. When B reaches point $A$, A is $30 \mathrm{~km}$ away from point $B$. Therefore, the distance between $A$ and $B$ is $\quad 90 \quad \mathrm{km}$.
【Solution】Solution: According to the problem, we have:
When they meet, A has traveled $\frac{4}{4+5}=\frac{4}{9}$ of the total distance, and B has traveled $1-\frac{4}{9}=\frac{5}{9}$ of the total distance;
After they meet, the speed ratio of A to B is $4 \times (1-25\%): 5 \times (1+20\%)=1: 2$;
When B reaches point $A$, B has traveled an additional $1-\frac{5}{9}=\frac{4}{9}$ of the total distance, and A has traveled an additional $\frac{4}{9} \times \frac{1}{2}=\frac{2}{9}$ of the total distance;
The distance between $A$ and $B$ is: $30 \div \left(1-\frac{4}{9}-\frac{2}{9}\right)=90(\mathrm{~km})$.
Answer: The distance between $A$ and $B$ is $90 \mathrm{~km}$.