Question

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 fuel consumption.

The Boeing 747-8 Intercontinental Jet can carry approximately 63,500 gallons of jet fuel, making it possible for the jet to travel 14,430 kilometers before needing to refuel.

Create a linear model that represents the amount of fuel on the plane, in gallons, as a function of the flight time, in hours.Show all of your work.



WRITER

Answer 1

To create a linear model that represents the amount of fuel on the plane, in gallons, as a function of the flight time, in hours, we need to find the rate of fuel consumption per hour.

From the given information, we know that the Boeing 747-8 Intercontinental Jet can travel 14,430 km before needing to refuel, and it can carry approximately 63,500 gallons of jet fuel.

Therefore, the rate of fuel consumption can be calculated as:

Rate of fuel consumption = Total fuel capacity ÷ Total distance traveled

= 63,500 gallons ÷ 14,430 km

To convert km to miles, we can use the conversion factor 1 km = 0.621371 miles.

Total distance = 16 hours × 550 miles per hour = 8,800 miles

So, the rate of fuel consumption can be calculated as:

Rate of fuel consumption = 63,500 gallons ÷ (14,430 km × 0.621371 miles/km)

= 63,500 gallons ÷ 8,949 miles

≈ 7.10 gallons per mile

Now, we can create a linear model that represents the amount of fuel on the plane, in gallons, as a function of the flight time, in hours, by using the following formula:

Fuel on plane = Total fuel capacity - (Rate of fuel consumption × Flight time)

Substituting the values we have calculated, we get:

Fuel on plane = 63,500 - (7.10 × Flight time)

Therefore, the linear model that represents the amount of fuel on the plane, in gallons, as a function of the flight time, in hours, is:

Fuel on plane = 63,500 - (7.10 × Flight time)