Let's break down the problem based on the image:

1. The blue car travels $45 \frac{1}{2}$ miles on $\frac{1}{4}$ gallons of gasoline.
2. The red car travels $22 \frac{2}{5}$ miles on $\frac{4}{5}$ gallons of gasoline.

Step 1: Convert mixed fractions to improper fractions

• For the blue car: $45 \frac{1}{2} = \frac{91}{2} \text{ miles}$
• For the red car: $22 \frac{2}{5} = \frac{112}{5} \text{ miles}$

Step 2: Calculate the unit rate (miles per gallon) for each car

The unit rate is calculated as the number of miles traveled per gallon of gasoline.

Blue car:

$\text{Unit rate} = \frac{\frac{91}{2} \text{ miles}}{\frac{1}{4} \text{ gallons}} = \frac{91}{2} \times \frac{4}{1} = \frac{364}{2} = 182 \text{ miles per gallon}$

Red car:

$\text{Unit rate} = \frac{\frac{112}{5} \text{ miles}}{\frac{4}{5} \text{ gallons}} = \frac{112}{5} \times \frac{5}{4} = \frac{112}{4} = 28 \text{ miles per gallon}$

Step 3: Compare the unit rates

• The blue car can travel 182 miles per gallon.
• The red car can travel 28 miles per gallon.

Therefore, the blue car can travel a greater distance on 1 gallon of gasoline.

Would you like further details on any part of this solution? Here are some related questions:

1. What is the difference in distance each car can travel with 1 gallon of gas?
2. How do mixed numbers get converted into improper fractions?
3. Can we calculate how much gasoline the blue car would need to travel 1 mile?
4. Why does the blue car have a much higher fuel efficiency than the red car?
5. How do these calculations relate to real-world fuel economy measurements?

Tip: When converting mixed numbers to improper fractions, remember to multiply the whole number by the denominator, then add the numerator.