Because the distance A walked after the meeting was equal to that before the meeting, when A arrived at A, the distance B walked after the meeting was equal to that before the meeting.

That is, when they met, A walked 2 kilometers more than B;

So the speed of A is (20/2+1)/2=5.5(km/h),

The speed of B is (20/2- 1)/2=4.5(km/h).

Method 2

Let the speed of a be xkm/h and the speed of b be ykm/h.

2x+2y=20

2x-2y=2

solve

x=5.5

y=4.5