Question

You are running a fuel economy study. One of the cars you find is blue. It can travel 28 1 2 miles on 1 1 4 gallons of gasoline. Another car is red. It can travel 21 3 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?

Answer 1

The unit rate for miles per gallon is 57 miles per gallon for the blue car and 87 miles per gallon for the red car.

The red car could travel a greater distance on 1 gallon of gasoline compared to the blue car.

Step-by-step explanation:

To find the unit rate for miles per gallon for each car, we need to divide the number of miles traveled by the number of gallons of gasoline used for each car.

For the blue car, it can travel 28½ miles on 1¼ gallons of gasoline, so the unit rate is: 28½ miles / 1¼ gallons.

To simplify this, we can convert 1¼ gallons to an improper fraction: 1 and ¼ = ¼ + ¼ = ½.

The unit rate is then 28½ miles / ½ gallon. To divide a fraction by another fraction, we can multiply the first fraction by the reciprocal of the second fraction.

So, the unit rate is: 28½ miles * 2/1 = 57 miles per gallon.

For the red car, it can travel 21¾ miles on 4¾ gallons of gasoline, so the unit rate is: 21¾ miles / 4¾ gallons.

To simplify this, we can convert 4¾ gallons to an improper fraction: 4 and ¾ = ¾ + ¾ + ¾ = ¾.

The unit rate is then 21¾ miles / ¾ gallon. To divide a fraction by another fraction, we can multiply the first fraction by the reciprocal of the second fraction.

So, the unit rate is: 21¾ miles * 4/1

= 87 miles per gallon.

To determine which car could travel the greater distance on 1 gallon of gasoline, we compare the unit rates.

The red car has a higher unit rate of 87 miles per gallon, while the blue car has a unit rate of 57 miles per gallon.

Therefore, the red car could travel a greater distance on 1 gallon of gasoline compared to the blue car.