To find out how much time Brianna has for each section, we need to divide the total time she has, which is \( \frac{5}{6} \) of an hour, by the number of sections, which is 3.
Calculating the time for each section:
\[ \text{Time per section} = \frac{\text{Total time}}{\text{Number of sections}} = \frac{\frac{5}{6}}{3} \]
Dividing by a whole number is the same as multiplying by its reciprocal:
\[ \frac{\frac{5}{6}}{3} = \frac{5}{6} \times \frac{1}{3} = \frac{5 \times 1}{6 \times 3} = \frac{5}{18} \]
So, the amount of time Brianna has to spend on each section is \( \frac{5}{18} \) of an hour.
Therefore, the answer is A) \( \frac{5}{18} \) hour.