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Let's break down the problem step by step.

We are given two cars, a blue one and a red one, and the task is to find the unit rate for each car in miles per gallon (mpg). Then, we will compare which car can travel the greater distance per gallon of gasoline.

### Blue Car:
- The blue car can travel \( 33 \frac{1}{2} \) miles using \( \frac{1}{4} \) gallons of gasoline.
- First, convert \( 33 \frac{1}{2} \) to an improper fraction:
  \[
  33 \frac{1}{2} = \frac{67}{2} \text{ miles}.
  \]
- To find the unit rate in miles per gallon, divide the miles by the gallons:
  \[
  \frac{67}{2} \div \frac{1}{4} = \frac{67}{2} \times 4 = \frac{268}{2} = 134 \text{ miles per gallon}.
  \]
  So, the blue car's unit rate is 134 miles per gallon.

### Red Car:
- The red car can travel \( 4 \frac{4}{5} \) miles using \( \frac{4}{5} \) gallon of gasoline.
- Convert \( 4 \frac{4}{5} \) to an improper fraction:
  \[
  4 \frac{4}{5} = \frac{24}{5} \text{ miles}.
  \]
- Now, find the unit rate in miles per gallon:
  \[
  \frac{24}{5} \div \frac{4}{5} = \frac{24}{5} \times \frac{5}{4} = \frac{24}{4} = 6 \text{ miles per gallon}.
  \]
  So, the red car's unit rate is 6 miles per gallon.

### Conclusion:
- The blue car has a unit rate of 134 miles per gallon.
- The red car has a unit rate of 6 miles per gallon.
- Therefore, the blue car can travel a greater distance on 1 gallon of gasoline.

Would you like further explanation or have additional questions?

Here are 5 questions related to this concept:
1. How do you convert mixed numbers to improper fractions?
2. What is the importance of unit rates in real-life applications like fuel efficiency?
3. How do you divide fractions and simplify results?
4. How could you solve similar problems using decimals instead of fractions?
5. What would the result be if the blue car's fuel efficiency changed to 50 miles on \( \frac{1}{4} \) gallons?

**Tip:** Always ensure to simplify fractions and mixed numbers to improper fractions for more straightforward calculations!

You are running a fuel economy study. One of the cars you find is blue. It can travel 33 1/2 miles on 1/4 gallons of gasoline. Another car is red. It can travel 4 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?

Learn how to calculate unit rates in miles per gallon by comparing two cars with fractional distances and fuel amounts. This problem explores the division of fractions and conversion of mixed numbers, making it ideal for middle school students in Grades 6-8.

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