To find Sierra's unit rate of miles per gallon, we need to divide the total number of miles driven by the total number of gallons of gas used.
Sierra drove 325 1/2 miles, which can be converted to an improper fraction: \[ 325 \frac{1}{2} = 325 + \frac{1}{2} = \frac{650}{2} + \frac{1}{2} = \frac{651}{2} \]
She used 15 1/2 gallons of gas, which can also be converted to an improper fraction: \[ 15 \frac{1}{2} = 15 + \frac{1}{2} = \frac{30}{2} + \frac{1}{2} = \frac{31}{2} \]
Next, we calculate the unit rate by dividing the total miles by the total gallons: \[ \text{Unit rate} = \frac{\text{Total miles}}{\text{Total gallons}} = \frac{\frac{651}{2}}{\frac{31}{2}} \]
When dividing by a fraction, we multiply by its reciprocal: \[ = \frac{651}{2} \times \frac{2}{31} = \frac{651}{31} \]
Now, we perform the division \(651 \div 31\): \[ 651 \div 31 = 21 \]
Thus, the unit rate of miles per gallon is: \[ \boxed{21} \text{ miles per gallon} \]