Question

You are running a fuel economy study. One of the cars you find is blue. It can travel 44 1/2 gallons of gasoline. Another car is red. It can travel 25 3/5 on 4/5 gallons 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

Question:

You are running a fuel economy study. One of the cars you find is blue. It can travel
`44(1)/(2)` miles on
`1(1)/(4)` gallons of gasoline.

Another car is red. It can travel
`25(3)/(5)` 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:

(a)

`Rate = 35(3)/(5)\ miles\ per\ gallon`

`Rate = 32\ miles\ per\ gallon`

(b)

The blue car will travel faster

Explanation:

Given

Blue Car:

`Distance = 44(1)/(2)\ miles`

`Gasoline = 1(1)/(4)\ gallons`

Red Car

`Distance = 25(3)/(5)\ miles`

`Gasoline = (4)/(5)\ gallons`

Solving (a):

This is solved by dividing the distance travelled by the amount of gasoline.

i.e.

`Rate = Distance/Gasoline`

Blue Car:

`Rate = 44(1)/(2) / 1(1)/(4)`

`Rate = (89)/(2) / (5)/(4)`

`Rate = (89)/(2) * (4)/(5)`

`Rate = (89)/(1) * (2)/(5)`

`Rate = (89 * 2)/(1 * 5)`

`Rate = (178)/(5)`

`Rate = 35(3)/(5)\ miles\ per\ gallon`

Red Car:

`Rate = 25(3)/(5)/(4)/(5)`

`Rate = (128)/(5)/(4)/(5)`

`Rate = (128)/(5) * (5)/(4)`

`Rate = (128 * 5)/(5 * 4)`

`Rate = (128)/(4)`

`Rate = 32\ miles\ per\ gallon`

(b)

In (a), we have:

`Rate = 35(3)/(5)\ miles\ per\ gallon` --- Blue Car

`Rate = 32\ miles\ per\ gallon` --- Red Car

By comparison:

The rate of the blue car is greater than that of the red

Hence, the blue car will travel faster