# The Long Haul

## The Situation

Two cars travel a distance of 100km. Both cars consume a different amount of fuel.

The first car, a Honda Civic, has a fuel tank that can hold 100L, and consumes 6L of fuel per 10 kilometers. The second car, a Dodge Ram, has a fuel tank that can hold 85L of fuel, and consumes 4L of fuel per 10 kilometers.

Note: The data has nothing to do with the actual fuel efficiency of these cars. The data used in this situation is data that I have created myself, and has nothing to do with the actual cars. The names are just there for the purpose of clarity.

## Classification Of Variables

The two main variables described in this situation are distance and amount of fuel.

• Distance describes how far the car has moved in kilometers. This will be described with the variable d.
• Amount of Fuel Remaining describes how much fuel the car has remaining in liters. This will be described with the variable f.

The f intercept describes the amount of fuel the car when it has not traveled any distance.

The d intercept essentially means the car has run out of fuel, because when a point intercepts with the x, or d axis in this case, it implies that y, or in this case, f, is equal to zero.

## Table Of Values

This link will direct you to a Google Spreadsheet, containing a table of values for both cars.

## Equations Of The Lines

To easily plot this situation graphically, we can create equations for both lines. We will

use Slope Y-Intercept form for this.

Honda Civic:

f = -0.6d + 100

Dodge Ram:

f= -0.4d + 85

We can check these equations by plotting in points. For the Honda Civic, we will take the point (10, 96).

Work:

f = -0.6d + 100

96= -0.6(10) + 100

96 = -6 + 100

96 = 96

L.S = R.S

For the Dodge Ram, we will take the point (10, 81).

Work:

f= -0.4d + 85

81= -0.4(10) + 85

81= -4 + 85

81 = 81

L.S = R.S

## Graph

To access the graph, just click the link above.

## Significance Of Point Of Intersection

The point of intersection represents the distance at which the two cars have the same

amount of fuel in their tank.

This occurs at a distance of 75 kilometers, where the cars have 55L of fuel left in their fuel tank. To put this in point form, it would be (75, 55).

We can confirm this is the point of intersection by inputting this point into both equations and seeing if it works.

Honda Civic:

f = -0.6d + 100

55= -0.6(75) + 100

55= -45 + 100

55 = 55

L.S = R.S

Dodge Ram:

f= -0.4d + 85

55= -0.4(75) + 85

55= -30 + 85

55 = 55

L.S = R.S

As you can see, this point does lie across both lines, meaning that it is the point of intersection.

Car buyers can use this point of intersection to choose what car to buy. If the car-buyer's job demands long car trips, it would be more fuel efficient to choose the Dodge Ram, based on the graph. If the buyer is using the car casually, and goes on short car trips, the Honda Civic would be the better choice here. It is up to the buyer on which to choose.

## Summary

After 75 kilometers of travelling, the two cars will both have 55L of fuel remaining in their fuel tanks.