ffmpeg encode video with different rates

ffmpeg encode video with different rates

I have two videos. I make this videos with the following codes:
ffmpeg -r 5 -f image2 -i "b%d.png" -c:v mpeg4 -q:v 5 -an a.avi
ffmpeg -r 15 -f image2 -i "b%d.png" -c:v mpeg4 -q:v 5 -an b.avi
As you can see, the only difference is the rate. Now I want to concatenate
them. Following the other post I use this:
ffmpeg -i "concat:a.avi|b.avi" -c copy movie2.avi
However the resulting movie shows the "b.avi" part much more slower.
Actually no difference of speed is appreciated between "a" and "b" parts.
How can I keep the differences of speed in the resulting movie?
Maybe I have some conceptual misunderstanding about rate... but the thing
is that I want the "b.avi" part to be faster than the "a.avi" part.