To find the unit rate for each car in miles per gallon, we need to divide the distance each car can travel by the amount of gasoline it consumes.
For the Blue Car:
- Distance: \( 40 \frac{1}{2} \) miles = \( \frac{81}{2} \) miles (since \( 40 \frac{1}{2} = 40.5 = \frac{81}{2} \))
- Gasoline: \( 1 \frac{1}{4} \) gallons = \( \frac{5}{4} \) gallons (since \( 1 \frac{1}{4} = 1.25 = \frac{5}{4} \))
Now, we'll calculate the unit rate (miles per gallon):
\[ \text{Unit Rate for Blue Car} = \frac{\text{Distance}}{\text{Gasoline}} = \frac{\frac{81}{2}}{\frac{5}{4}} \]
To divide by a fraction, multiply by its reciprocal:
\[ \frac{\frac{81}{2}}{\frac{5}{4}} = \frac{81}{2} \times \frac{4}{5} = \frac{81 \times 4}{2 \times 5} = \frac{324}{10} = \frac{162}{5} = 32.4 \text{ miles per gallon} \]
For the Red Car:
- Distance: \( 28 \frac{4}{5} \) miles = \( \frac{144}{5} \) miles (since \( 28 \frac{4}{5} = 28.8 = \frac{144}{5} \))
- Gasoline: \( \frac{4}{5} \) gallons
Now, we'll calculate the unit rate for the red car:
\[ \text{Unit Rate for Red Car} = \frac{\text{Distance}}{\text{Gasoline}} = \frac{\frac{144}{5}}{\frac{4}{5}} \]
Again, divide by multiplying by the reciprocal:
\[ \frac{\frac{144}{5}}{\frac{4}{5}} = \frac{144}{5} \times \frac{5}{4} = \frac{144 \times 5}{5 \times 4} = \frac{144}{4} = 36 \text{ miles per gallon} \]
Summary:
- Unit Rate for the Blue Car: \( \frac{162}{5} \) or \( 32.4 \) miles per gallon.
- Unit Rate for the Red Car: \( 36 \) miles per gallon.
Conclusion:
The red car can travel a greater distance on 1 gallon of gasoline.