obviously it is not right. first, you have one answer, they asked for the rate of each, which means you should have two answers. secondly, you have a negative answer. which makes no sense for this problem. were they cycling/jogging backwards?

go with your set up again. let R be the rate of the cyclist. then R - 6 is the rate of the jogger. if the cyclist takes T hours to cover a distance D, then the jogger takes 2T hours to cover the same distance.

now what equations would you set up?