Let's solve the problem regarding the unit rate for miles per gallon for each car.

For the Blue Car:

• Distance traveled = $35 \frac{1}{2}$ miles = $35.5$ miles.
• Gallons of gasoline = $\frac{1}{4}$ gallon.

The unit rate is the number of miles per gallon, which can be found by dividing the distance traveled by the amount of gasoline used: $\text{Unit rate for blue car} = \frac{35.5 \text{ miles}}{\frac{1}{4} \text{ gallon}} = 35.5 \times 4 = 142 \text{ miles per gallon}.$

For the Red Car:

• Distance traveled = $27 \frac{1}{5}$ miles = $27.2$ miles.
• Gallons of gasoline = $\frac{4}{5}$ gallon.

Similarly, the unit rate is: $\text{Unit rate for red car} = \frac{27.2 \text{ miles}}{\frac{4}{5} \text{ gallon}} = 27.2 \times \frac{5}{4} = 34 \text{ miles per gallon}.$

Summary:

• The blue car can travel 142 miles per gallon.
• The red car can travel 34 miles per gallon.

Would you like further clarification or details on any of these steps?

Here are 5 related questions to expand on this topic:

1. What would happen to the unit rate if the blue car used $\frac{1}{2}$ gallon instead of $\frac{1}{4}$?
2. How would the efficiency change if the red car’s gasoline consumption were halved?
3. What is the percentage difference in fuel efficiency between the two cars?
4. If the blue car traveled 50 miles, how much gasoline would it use?
5. How would you interpret these unit rates in terms of cost if gasoline were $3 per gallon?

Tip: When calculating unit rates or ratios, always divide the distance by the amount of fuel to obtain the fuel efficiency in miles per gallon.