It takes Angie 1/2 hour to mow 2/3 of lawn. How long will it take to mow entire lawn?

1 answer

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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