In random forest, what happens if I add features that are correlated? I'm training a random forest, trying to predict market shares of future stores on geographical areas. I have many features for these areas, some of which tell similar but different things about one thing. 

For example, I know the total number of $accommodations$ in the area, and I also have 5 others columns which are all linked in the following way: 

$main \space accommodations + secondary \space accommodations + holiday \space accommodations = houses + flats = accommodations$

I have the feeling that including them all in my model would be wrong... but including them might be important... Any hint on how I should handle this?

Would it be a good idea to include $accommodations$ as absolute value and include all the other five but as % (of $accommodations$) and not as absolute values?

In a similar fashion, I also have the total number of $households$ of the area, the $total \space income$ of the area, and the $average \space income$ of households in the area (so that $households * average \space income = total \space income$). I have the feeling using the average and not the total income would be a better idea, but how can I be sure I'm right ?

(I guess I could train three random forests using the average income only, the total income only, and both, and see how they perform on cross validation, but is there a rule of thumb that I should know of which can make me go faster ?)

(In case it's relevant, I'm using R and the randomForest package)
Random forests don't suffer from correlated variables like linear regression models do. Random forests randomly pick from a subset of variables at each split (hence the "random" in "random forests"). This means that correlated variables are less likely to show up together when the trees are being trained. But even when correlated variables show up in the same random subset of variables, it's still not much of an issue because the variables aren't assigned coefficients. 

Correlated variables are mostly an issue for linear models that try to hold all other variables constant when calculating coefficients during training. The variable selection process is much simpler for trees and tree-based algorithms like random forests and gradient boosting. When a random forest is being trained and a tree's split is being evaluated, the algorithm will simply pick whichever feature most reduces error on that particular split of the tree. Once a variable is picked, there is no coefficient, just a greater-than/less-than split point, so the problem of "exploding coefficients" doesn't apply.