To find the unit rate of how long it takes Brynn to mow the entire lawn, we first need to determine how long it would take her to mow the entire lawn based on the amount mowed in 1/2 hour.
Brynn has mowed \( \frac{2}{3} \) of the lawn in \( \frac{1}{2} \) hour. We can set up a proportion to find out how long it will take to mow the full lawn (1 whole).
Let \( t \) be the time in hours it will take to mow the entire lawn. The proportion can be expressed as follows:
\[ \frac{2/3}{1} = \frac{1/2}{t} \]
Now we will cross-multiply to solve for \( t \):
\[ 2/3 \cdot t = 1/2 \]
Next, we can solve for \( t \) by multiplying both sides by the reciprocal of \( \frac{2}{3} \):
\[ t = \frac{1/2}{2/3} \]
Now we multiply by the reciprocal of \( \frac{2}{3} \):
\[ t = \frac{1}{2} \cdot \frac{3}{2} = \frac{3}{4} \]
Thus, it will take Brynn \( \frac{3}{4} \) hour to mow the entire lawn.
To convert \( \frac{3}{4} \) hour into minutes, we can multiply by 60 (as there are 60 minutes in an hour):
\[ \frac{3}{4} \cdot 60 = 45 \]
So, it will take Brynn 45 minutes to mow the entire lawn.
The answer is that it will take Brynn 45 minutes to mow the entire lawn.