Question

You are running a fuel economy study. One of the cars you find is blue. It can travel 40 and one half miles
on 1 and one fourth gallons
of gasoline. Another car is red. It can travel 28 and four fifths miles
on four fifths 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?
Question content area bottom
Part 1
The unit rate for the blue car is
  
enter your response here ​mile(s) per gallon.
​(Simplify your answer. Type an​ integer, proper​ fraction, or mixed​ number.)

Answer 1

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.