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 find out how much gasoline the plane consumes per hour. We can do this by dividing the total amount of gasoline it can carry by the maximum distance it can travel before refueling.
Gasoline consumption rate = (Total gasoline capacity) / (Maximum distance)
Gasoline consumption rate = 422,000 gallons / 14,430 kilometers
Gasoline consumption rate = 29.21 gallons per kilometer
Now, we need to find out how many kilometers the plane travels per hour. To do this, we must find out its cruising speed. According to Boeing, the 747-8 Intercontinental Jet has a cruising speed of approximately 920 km/h.
Now we can find out the amount of gasoline the plane consumes per hour:
Gasoline consumption per hour = (Gasoline consumption rate) x (Cruising speed)
Gasoline consumption per hour = 29.21 gallons/km x 920 km/h
Gasoline consumption per hour = 26,873.2 gallons/h
Now that we know the gasoline consumption per hour, we can create a linear model.
Let G(t) be the amount of gasoline on the plane, in gallons, after t hours of flight. We start with a full tank of 422,000 gallons, and we lose 26,873.2 gallons per hour.
Therefore, our linear model is:
G(t) = 422,000 - 26,873.2t
where t is the flight time in hours.