Sheleah and her family are planning a trip from Los Angeles, California to Melbourne, Australia. While booking her family's plane tickets, she notices on the itinerary that the airline is offering a sixteen hour straight flight from Los Angeles to Melbourne on a Boeing 747-8 Intercontinental Jet. In an effort to learn more about the capabilities of the Jet, Sheleah does a little research and stumbles upon the following graph and facts about the Jet's gasoline consumption.
The Boeing 747-8 Intercontinental Jet can carry approximately 422,000 gallons of gasoline, making it possible for the jet to travel 14,430 kilometers before needing to refuel.
Create a linear model that represents the amount of gasoline on the plane, in gallons, as a function of the flight time, in hours. Show all of your work.
First, we need to determine how fast the jet is consuming gasoline per hour. To find this, we can first determine how many hours it takes the jet to travel 14,430 kilometers.
The speed of a Boeing 747-8 Intercontinental Jet is approximately 900 km/hr. Therefore, to determine how many hours it takes to travel 14,430 km, we can use the equation:
Time (in hours) = Distance (in kilometers) / Speed (in kilometers per hour)
Time (in hours) = 14,430 km / 900 km/hr
Time (in hours) ≈ 16 hours
Now that we know it takes approximately 16 hours for the jet to consume 422,000 gallons of gasoline, we can determine the rate of gasoline consumption per hour by dividing the total amount of gasoline by the number of hours:
Gasoline consumption per hour = Total amount of gasoline (in gallons) / Time (in hours)
Gasoline consumption per hour = 422,000 gallons / 16 hours
Gasoline consumption per hour ≈ 26,375 gallons/hour
Now that we have the rate of gasoline consumption per hour, we can create a linear model that represents the amount of gasoline on the plane, in gallons, as a function of the flight time, in hours. The equation for a linear model is y = mx + b, where m is the slope and b is the y-intercept.
In this case, the slope (m) represents the rate of gasoline consumption per hour, which is -26,375 gallons/hour (negative because the amount of gasoline decreases over time). The y-intercept (b) represents the initial amount of gasoline on the plane, which is 422,000 gallons.
Therefore, our linear model is:
y = -26,375x + 422,000
This equation represents the amount of gasoline on the plane (y), in gallons, as a function of the flight time (x), in hours.