1. Mathematica is case sensitive. Type solve instead of Solve and you will get no helpful message "Are you sure you didn't mean Solve instead of solve?!?!?" from Mathematica. When it doesn't understand it will sometimes just give it back to you and expect you to figure it out for yourself. Someday that may change.
2. Solve works fairly well for polynomial problems and often badly or not at all for other kinds of problems and Mathematica does not warn you about this. Reduce sometimes does better for non-polynomial problems.
3. Even the simpler problem
Reduce[(w m)^1/(a-1) + (w r)^1/(a-1) == 1, w]
does not show any sign of progress in reasonable time.
4. The much simpler problem
Reduce[(w m)^1/(a-1) == 1, w]
does quickly show you a solution and might give some idea how complicated Mathematica can make a problem.
That shows that Mathematica is thinking not only of Real values, but also Complex values and all combinations of those.
5. If you can provide additional information to Reduce, like
Reduce[(w m)^1/(a-1) == 1 && m>0 && a>1, w]
then this may make finding a solution possible or impossible, may speed up or even slow down the process. v>0 is sufficient to get Mathematica to realize that you intend v to be a Real variable.
6. Be very careful with subscripts and trying to desktop publish your Mathematica input. Trying to do that is an unending source of problems for users.