To solve the problem in the image:

Step 1: Blue Car's Unit Rate

The blue car travels $35 \frac{1}{2}$ miles on $1 \frac{1}{4}$ gallons of gasoline.

1. Convert the mixed numbers into improper fractions: $35 \frac{1}{2} = \frac{71}{2}, \quad 1 \frac{1}{4} = \frac{5}{4}$

2. To find the unit rate (miles per gallon), divide the total miles by the total gallons: $\text{Unit rate for blue car} = \frac{\frac{71}{2}}{\frac{5}{4}} = \frac{71}{2} \times \frac{4}{5} = \frac{284}{10} = 28.4 \, \text{miles per gallon}.$

Step 2: Red Car's Unit Rate

The red car travels $28 \frac{4}{5}$ miles on $\frac{4}{5}$ gallons of gasoline.

1. Convert the mixed number into an improper fraction: $28 \frac{4}{5} = \frac{144}{5}$

2. To find the unit rate (miles per gallon), divide the total miles by the total gallons: $\text{Unit rate for red car} = \frac{\frac{144}{5}}{\frac{4}{5}} = \frac{144}{5} \times \frac{5}{4} = \frac{144}{4} = 36 \, \text{miles per gallon}.$

Step 3: Compare

• Blue car: $28.4 \, \text{miles per gallon}$
• Red car: $36 \, \text{miles per gallon}$

Conclusion: The red car can travel a greater distance on 1 gallon of gasoline.

Let me know if you'd like a deeper explanation or visualized calculations!
Here are five related questions to consider:

1. How would these calculations change if we used different units (e.g., kilometers)?
2. What happens if the fuel consumption of one car is doubled?
3. How can mixed fractions affect real-world problem-solving accuracy?
4. Can we model these unit rates graphically to show their differences?
5. What external factors might affect real-world fuel efficiency?

Tip: Always simplify fractions in real-world calculations to make interpretation easier!