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The problem describes a fuel economy study comparing two cars: a blue car and a red car. Here's how we can break it down to find the unit rate (miles per gallon) for each car.

### Given:
- The blue car can travel 4½ miles on 1¼ gallons of gasoline.
- The red car can travel 20⅘ miles on 4/5 gallons of gasoline.

### To find:
1. The unit rate for each car (miles per gallon).
2. Which car can travel the greater distance on 1 gallon of gasoline.

---

#### **Step 1: Blue Car Calculation**
The blue car travels 4½ miles using 1¼ gallons of gasoline.

1. Convert mixed numbers to improper fractions:
   - \( 4 \frac{1}{2} = \frac{9}{2} \) miles
   - \( 1 \frac{1}{4} = \frac{5}{4} \) gallons

2. To find the unit rate (miles per gallon), divide the miles traveled by the gallons used:
   \[
   \text{Unit rate for blue car} = \frac{\frac{9}{2}}{\frac{5}{4}} = \frac{9}{2} \times \frac{4}{5} = \frac{36}{10} = 3.6 \, \text{miles per gallon}
   \]

#### **Step 2: Red Car Calculation**
The red car travels 20⅘ miles using 4/5 gallons of gasoline.

1. Convert the mixed number to an improper fraction:
   - \( 20 \frac{4}{5} = \frac{104}{5} \) miles

2. To find the unit rate (miles per gallon), divide the miles traveled by the gallons used:
   \[
   \text{Unit rate for red car} = \frac{\frac{104}{5}}{\frac{4}{5}} = \frac{104}{5} \times \frac{5}{4} = \frac{104}{4} = 26 \, \text{miles per gallon}
   \]

---

#### **Step 3: Comparison**
- The blue car travels 3.6 miles per gallon.
- The red car travels 26 miles per gallon.

Clearly, the **red car** can travel the greater distance on 1 gallon of gasoline.

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Let me know if you'd like more details or have any questions!

### Here are 5 follow-up questions:
1. How would you calculate the cost of driving each car for a specific distance if you know the price per gallon?
2. What is the significance of simplifying fractions when calculating unit rates?
3. How can understanding unit rates help compare other real-world scenarios like fuel efficiency or speed?
4. Can you explain how mixed numbers are converted into improper fractions?
5. How would these calculations change if the cars were electric, using kilowatt-hours instead of gasoline?

### Tip: 
When dividing fractions, always remember to multiply by the reciprocal of the divisor for accurate results!

You are running a fuel economy study. One of the cars you find is blue. It can travel 4 1/2 miles on 1 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 can travel the greater distance on 1 gallon of gasoline?

This problem compares two cars—blue and red—by calculating their unit rates in miles per gallon. The blue car travels 4½ miles on 1¼ gallons, and the red car travels 20⅘ miles on 4/5 gallon. Learn how to convert mixed numbers into improper fractions and solve for fuel efficiency.

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