Sierra is driving her truck across the country. Today she drove 325 1/2 miles and used 15 1/2 gallons of gas. What is her unit rate of miles per gallon?

1 answer

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: \[ \boxed{21} \text{ miles per gallon} \]