To find the unit rate of miles per gallon, you divide the total miles driven by the number of gallons the car can hold.
Valerie can drive 288 miles on a full tank which holds 16 gallons.
So, the calculation is:
\[ \text{Unit rate} = \frac{\text{Total miles}}{\text{Total gallons}} = \frac{288 \text{ miles}}{16 \text{ gallons}} = 18 \text{ miles per gallon} \]
Thus, the unit rate is 18 miles per gallon.