The first information we're given is, the plant grows by 1 1/6 inches per week. We are to determine the number of weeks in order for the height to be 6 1/6 inches. Using the dimensional analysis approach, the solution is as follows:
6 1/6 inches * 1 week/1 1/6 inches = 5.286 weeks
Thus, the it takes between 5 to 6 weeks before the plant can be 6 1/6 inches high.