To find the unit rate for miles per gallon for each car, we need to divide the distance traveled by the amount of gasoline used.
Blue Car:
- Distance: \( 40 \frac{1}{2} \) miles = \( 40.5 \) miles
- Gasoline: \( 1 \frac{1}{4} \) gallons = \( 1.25 \) gallons
Calculating Unit Rate for Blue Car: \[ \text{Miles per gallon} = \frac{\text{Distance}}{\text{Gasoline}} = \frac{40.5 \text{ miles}}{1.25 \text{ gallons}} \]
To perform the division: \[ \frac{40.5}{1.25} = 40.5 \div 1.25 \] Calculating this, we can multiply by 100 to eliminate the decimals: \[ 40.5 \div 1.25 = \frac{40.5 \times 100}{1.25 \times 100} = \frac{4050}{125} \]
Now, simplifying \( \frac{4050}{125} \): \[ 4050 \div 125 = 32.4 \]
So, the unit rate for the blue car is: \[ \text{32.4 miles per gallon} \]
Red Car:
- Distance: \( 24 \frac{4}{5} \) miles = \( 24.8 \) miles
- Gasoline: \( \frac{4}{5} \) gallons
Calculating Unit Rate for Red Car: \[ \text{Miles per gallon} = \frac{\text{Distance}}{\text{Gasoline}} = \frac{24.8 \text{ miles}}{\frac{4}{5} \text{ gallons}} \]
To perform the division, we can multiply by the reciprocal: \[ \frac{24.8}{\frac{4}{5}} = 24.8 \times \frac{5}{4} = \frac{24.8 \times 5}{4} = \frac{124}{4} = 31 \]
So, the unit rate for the red car is: \[ \text{31 miles per gallon} \]
Conclusion:
- The unit rate for the blue car is 32.4 miles per gallon.
- The unit rate for the red car is 31 miles per gallon.
The blue car could travel the greater distance on 1 gallon of gasoline since 32.4 miles per gallon is greater than 31 miles per gallon.