Question

Stanley drove his car on a business trip when he left, the mileage was 840 miles, and when he returned, the mileage was 1,200 miles. The car used 12 gallons of gasoline for this trip.

Carla made the same trip as Stanley, but her car used only 10 gallons of gasoline. How do the slopes for Stanley's and Carla's cars compare?

Answer 1

Stanley's unit rate is 30 miles per gallon ( represented by: $y=30x$ )
Carla's unit rate is 36 miles per gallon ( represented by: $y=36x$ )

Carla's unit rate is higher than Stanley's. (mention the slope being steeper on the graph, because I have the same vacation homework.)

Answer 2

The comparison of the fuel consumption slopes is required.

The slope of Carla is $1.2$ times more than Stanley's.

Let $x$ represent the gallons

$y$ represent the miles driven

Slope is given by

$m=\dfrac{\Delta y}{\Delta x}$

The slope of Stanley is

$m_s=\dfrac{1200-840}{12}=30$

So, Stanley drives 30 miles for 1 gallon of gasoline.

The slope of Carla is

$m_c=\dfrac{1200-840}{10}=36$

So, Carla drives 36 miles for 1 gallon of gasoline.

$\dfrac{m_c}{m_s}=\dfrac{36}{30}\\\Rightarrow m_c=1.2m_s$

The slope of Carla is $1.2$ times more than Stanley's.

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