To find out how long it will take Angie to mow the entire lawn, we first need to determine her mowing rate.
Angie mows \( \frac{2}{3} \) of the lawn in \( \frac{1}{2} \) hour.
To find her mowing rate, we can calculate how long it would take her to mow the entire lawn. If it takes her \( \frac{1}{2} \) hour to mow \( \frac{2}{3} \) of the lawn, we can set up a proportion to find out how long it takes to mow 1 whole lawn.
Let \( t \) be the time it takes to mow the entire lawn. We have the ratio:
\[ \frac{2/3}{1} = \frac{1/2}{t} \]
Cross-multiplying gives:
\[ 2/3 \cdot t = 1/2 \]
Now solve for \( t \):
\[ t = \frac{1/2}{2/3} \]
To divide by a fraction, multiply by its reciprocal:
\[ t = \frac{1}{2} \times \frac{3}{2} = \frac{3}{4} \]
So, it will take Angie \( \frac{3}{4} \) hour to mow the entire lawn.
To convert \( \frac{3}{4} \) hour into minutes, multiply by 60:
\[ \frac{3}{4} \times 60 = 45 \text{ minutes} \]
Therefore, it will take Angie 45 minutes to mow the entire lawn.
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