To find Jacob's unit rate in miles per minute, we can start with the information given: Jacob skates \( \frac{3}{10} \) of a mile in \( \frac{1}{2} \) of a minute.
We can calculate his speed in miles per minute by dividing the distance he skates by the time it takes.
The formula for speed or unit rate is:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
Substituting in the values we have:
\[ \text{Speed} = \frac{\frac{3}{10} \text{ miles}}{\frac{1}{2} \text{ minute}} \]
To divide by a fraction, we multiply by the reciprocal:
\[ \text{Speed} = \frac{3}{10} \times \frac{2}{1} = \frac{3 \times 2}{10 \times 1} = \frac{6}{10} \text{ miles per minute} \]
We can simplify \( \frac{6}{10} \):
\[ \frac{6}{10} = \frac{3}{5} \]
Therefore, Jacob's unit rate is \( \frac{3}{5} \) miles per minute, or 0.6 miles per minute.