1. The problem statement, all variables and given/known data The population of a country is divided in two groups: People who live in rural areas (R(t)) and people who live in urban areas (U(t)). People move from rural to urban areas with a rate m and from urban to rural areas with rate n. a) Introduce the fraction of people (Z(t)) who live in rural areas as a new variable and derive an equation for it. b) Find the steady state(s) of the equation for Z and the stability condition. 2. Relevant equations R' = −mR + nU U' = mR − nU. 3. The attempt at a solution a) So I don't really get this, but is the fraction Z(t) different from R(t)?? Anyways, I think it goes: Z(t) = R(t) - U(t) / R(t) how would i go about deriving it? I am extremely confused. If anyone can just somehow reword it or something so that I can understand it that would be great. b) If I could get Z(t) into differential form I can easily find the steady state, by just setting it = to 0.. so my problem really lies in the first part.