Question

Kate is lining up logs across a pool for a boom run. The logs are 2/3 meter long. The distance across the pool is 5 meters. The distance left to fill the pool is 1/3. What fraction of a log can Kate use to fill the remaining 1/3 meter?

Answer 1

To determine how much of a log Kate can use to fill the remaining \( \frac{1}{3} \) meter, we first note that each log is \( \frac{2}{3} \) meter long.

We need to find what fraction of one log corresponds to \( \frac{1}{3} \) meter. We set up a proportion to do this:

\[
\text{Length of one log} = \frac{2}{3} \text{ meter}
\]

Let \( x \) be the fraction of the log needed to fill \( \frac{1}{3} \) meter. Then we have the equation:

\[
x \cdot \frac{2}{3} = \frac{1}{3}
\]

To solve for \( x \), we can multiply both sides of the equation by \( 3 \):

\[
3 \cdot x \cdot \frac{2}{3} = 3 \cdot \frac{1}{3}
\]

This simplifies to:

\[
2x = 1
\]

Now, dividing both sides by \( 2 \):

\[
x = \frac{1}{2}
\]

Thus, Kate can use \( \frac{1}{2} \) of a log to fill the remaining \( \frac{1}{3} \) meter.

The final answer is:

\[
\frac{1}{2}
\]