Conditional Formatting and Rules for a cell

Is there a way to use conditional formatting & rules in one cell where you can check if the contents of another cell is "ROI" and the number in the current cell is <16 you shade it green, if the number is >16<30 then shade it yellow, and if it's >31 then shade it yellow.   If the other cell equals "eFile" and the number in the current cell is <30 shade it green, if the number >31 shade it red.  

So it basically the cell with the formatting has a number of days in it and if the 2nd cell has ROI then it uses one set of shading rules based on number, but if the other cell has eFile than uses a different set of shading rules.  

Can this be done?