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The problem involves calculating the fuel efficiency of two cars (blue and red) in terms of miles per gallon, based on their given fuel consumption and distance traveled.

### Blue Car:
- The blue car travels \( \frac{1}{2} \) miles on \( \frac{1}{4} \) gallons of gasoline.

To find the unit rate (miles per gallon), we divide the distance by the amount of fuel consumed:

\[
\text{Miles per gallon for the blue car} = \frac{\frac{1}{2}}{\frac{1}{4}} = \frac{1}{2} \times \frac{4}{1} = 2 \text{ miles per gallon}.
\]

### Red Car:
- The red car travels \( 20 \frac{4}{5} \) miles on \( \frac{4}{5} \) gallons of gasoline. 
First, convert the mixed number \( 20 \frac{4}{5} \) to an improper fraction:
\[
20 \frac{4}{5} = \frac{100}{5} + \frac{4}{5} = \frac{104}{5} \text{ miles}.
\]

Now, divide this distance by the fuel consumed:

\[
\text{Miles per gallon for the red car} = \frac{\frac{104}{5}}{\frac{4}{5}} = \frac{104}{5} \times \frac{5}{4} = \frac{104}{4} = 26 \text{ miles per gallon}.
\]

### Conclusion:
- The blue car has a fuel efficiency of **2 miles per gallon**.
- The red car has a fuel efficiency of **26 miles per gallon**.

Thus, the red car can travel a greater distance on 1 gallon of gasoline.

Let me know if you want further details or have any questions!

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Here are 5 related questions for deeper understanding:
1. How would the unit rate change if the blue car used \( \frac{1}{3} \) gallons of gasoline instead of \( \frac{1}{4} \)?
2. Can you calculate the distance the red car would travel on 2 gallons of gasoline?
3. If the blue car had a fuel efficiency of 4 miles per gallon, how much fuel would it need to travel 8 miles?
4. How does the concept of a unit rate apply to real-world fuel economy ratings?
5. What is the mathematical method for converting mixed numbers to improper fractions?

**Tip**: When dividing fractions, remember that division is the same as multiplying by the reciprocal of the divisor.

You are running a fuel economy study. One of the cars you find is blue. It can travel 1/2 miles on 1/4 gallons of gasoline. Another car is red. It can travel 20 4/5 miles on 4/5 gallon of gasoline. What is the unit rate for miles per gallon for each car? Which car could travel the greater distance on 1 gallon of gasoline?

Find out how to calculate the unit rate of miles per gallon for two cars with different fuel efficiencies. The blue car travels 1/2 miles using 1/4 gallons, while the red car covers 20 4/5 miles with 4/5 gallons. Learn which car travels farther per gallon of fuel, suitable for Grades 6-8.

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