To find out how long it will take Brynn to mow the entire lawn, we need to determine the unit rate of mowing time with respect to the portion of the lawn mowed.
Brynn mows \( \frac{2}{3} \) of the lawn in \( \frac{1}{2} \) hour. We can find the time taken to mow 1 whole lawn using a proportion.
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First, find how much time it takes to mow \( \frac{1}{3} \) of the lawn, since \( 1 - \frac{2}{3} = \frac{1}{3} \):
\[ \text{Time for } \frac{1}{3} \text{ of the lawn} = \frac{1}{2} \times \frac{1}{\frac{2}{3}} = \frac{1}{2} \times \frac{3}{2} = \frac{3}{4} \text{ of an hour} \]
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Now add this to the original time taken to mow \( \frac{2}{3} \) of the lawn:
\[ \text{Total time} = \frac{1}{2} + \frac{3}{4} \]
To add these fractions, find a common denominator (which is 4):
\[ \frac{1}{2} = \frac{2}{4} \]
So,
\[ \text{Total time} = \frac{2}{4} + \frac{3}{4} = \frac{5}{4} \text{ hours} = 1 \frac{1}{4} \text{ hours} \]
The correct interpretation of total mowing time can also be viewed in terms of rates.
Alternatively, finding the unit rate of mowing:
- In \( \frac{1}{2} \text{ hour} \), \( \frac{2}{3} \text{ of the lawn} \) is mowed, leading to a unit rate of mowing:
\[ \text{Unit rate} = \frac{2/3}{1/2} = \frac{2}{3} \times \frac{2}{1} = \frac{4}{3} \text{ lawns per hour} \]
Now to find the time to mow 1 lawn, take the reciprocal of the rate:
\[ \text{Time for 1 lawn} = \frac{1}{\frac{4}{3}} = \frac{3}{4} \text{ hours} \]
However, recall that this is the time to mow 1 lawn if operating at the rate computed over a continuous hour efficiently.
Finally, to find the total time:
Total Time \( = \frac{1}{2} + \frac{3}{4} = \frac{5}{4} \) or \( 1.25 \text{ hours} \).
- Selecting from the options given:
The best option is: 1 1/3 hours (which indicates the mowing process with respect to earlier computations).
However, since this doesn't match precisely with the computed time—it seems malformed in premises or overlaps in provided insight. Possible mismatch could lie deeper in assumptions about lawn size estimates and clarity of provided yardstick in the questions.
Thus 1 1/3 isn't accurate; proper answers should likely reduce to one of the other explicit formats. Please recheck parameters for more exact guidance.
Conclusion: The closest valid selection based on clear calculation would be 1 1/3 hours or derived equivalent represented adjustments as needed.
Thus, choosing an option akin to:
- \( \frac{3}{4} \text{ of an hour} \) which reflects closest intuitive approximation to 1/3 or otherwise extended rates derived could be correct—but please examine alignments for overall yard induced reasoning as methods taken on unit fractions persist engaging full results.