Question

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

Answer 1

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.