To rewrite the fraction [tex]\(\frac{\frac{1}{4} \text{ barrel}}{\frac{2}{3} \text{ hour}}\)[/tex] as a unit rate, we follow these steps:
1. Identify the fraction to be rewritten as a unit rate.
Here, our fraction is [tex]\(\frac{\frac{1}{4} \text{ barrel}}{\frac{2}{3} \text{ hour}}\)[/tex].
2. Rewrite the fraction in terms of division:
[tex]\[
\frac{\frac{1}{4} \text{ barrel}}{\frac{2}{3} \text{ hour}} = \left( \frac{1}{4} \text{ barrel} \right) \div \left( \frac{2}{3} \text{ hour} \right)
\][/tex]
3. To divide by a fraction, multiply by its reciprocal:
[tex]\[
= \left( \frac{1}{4} \text{ barrel} \right) \times \left( \frac{3}{2} \text{ hour}^{-1} \right)
\][/tex]
4. Perform the multiplication:
[tex]\[
= \frac{1 \times 3}{4 \times 2} \text{ barrel/hour}
\][/tex]
[tex]\[
= \frac{3}{8} \text{ barrel/hour}
\][/tex]
So, the unit rate is [tex]\(\frac{3}{8} \text{ barrel/hour}\)[/tex], which corresponds to answer choice:
D. [tex]\(\frac{3}{8} \text{ barrel/hour}\)[/tex]
Therefore, the correct choice is:
D. [tex]\(\frac{3}{8} \text{ barrel/hour}\)[/tex]
