Question:
You are running a fuel economy study. One of the cars you find is blue. It can travel [tex]44\frac{1}{2}[/tex] miles on [tex]1\frac{1}{4}[/tex] gallons of gasoline.
Another car is red. It can travel [tex]25\frac{3}{5}[/tex] on [tex]\frac{4}{5}[/tex] 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)
[tex]Rate = 35\frac{3}{5}\ miles\ per\ gallon[/tex]
[tex]Rate = 32\ miles\ per\ gallon[/tex]
(b)
The blue car will travel faster
Step-by-step explanation:
Given
Blue Car:
[tex]Distance = 44\frac{1}{2}\ miles[/tex]
[tex]Gasoline = 1\frac{1}{4}\ gallons[/tex]
Red Car
[tex]Distance = 25\frac{3}{5}\ miles[/tex]
[tex]Gasoline = \frac{4}{5}\ gallons[/tex]
Solving (a):
This is solved by dividing the distance travelled by the amount of gasoline.
i.e.
[tex]Rate = Distance/Gasoline[/tex]
Blue Car:
[tex]Rate = 44\frac{1}{2} / 1\frac{1}{4}[/tex]
[tex]Rate = \frac{89}{2} / \frac{5}{4}[/tex]
[tex]Rate = \frac{89}{2} * \frac{4}{5}[/tex]
[tex]Rate = \frac{89}{1} * \frac{2}{5}[/tex]
[tex]Rate = \frac{89 * 2}{1 * 5}[/tex]
[tex]Rate = \frac{178}{5}[/tex]
[tex]Rate = 35\frac{3}{5}\ miles\ per\ gallon[/tex]
Red Car:
[tex]Rate = 25\frac{3}{5}/\frac{4}{5}[/tex]
[tex]Rate = \frac{128}{5}/\frac{4}{5}[/tex]
[tex]Rate = \frac{128}{5} * \frac{5}{4}[/tex]
[tex]Rate = \frac{128 * 5}{5 * 4}[/tex]
[tex]Rate = \frac{128}{4}[/tex]
[tex]Rate = 32\ miles\ per\ gallon[/tex]
(b)
In (a), we have:
[tex]Rate = 35\frac{3}{5}\ miles\ per\ gallon[/tex] --- Blue Car
[tex]Rate = 32\ miles\ per\ gallon[/tex] --- Red Car
By comparison:
The rate of the blue car is greater than that of the red
Hence, the blue car will travel faster
