Final answer:
The linear model representing the amount of gasoline on the plane, in gallons, as a function of the flight time, in hours, is: Gasoline = FCR * Time
Step-by-step explanation:
To create a linear model that represents the amount of gasoline on the plane, in gallons, as a function of the flight time, in hours, we can use the given information to establish a relationship between the two variables.
Given:
- The Boeing 747-8 Intercontinental Jet can carry approximately 422,000 gallons of gasoline.
- The jet can travel 14,430 kilometers before needing to refuel.
To create the linear model, we need to determine the rate at which the gasoline is consumed over time.
1. Convert the distance traveled from kilometers to miles, as the fuel capacity is given in gallons and the typical fuel consumption rate is in miles per gallon.
14,430 kilometers ≈ 8,964 miles (approximate conversion)
2. Divide the total fuel capacity (422,000 gallons) by the total distance traveled (8,964 miles) to find the fuel consumption rate in gallons per mile.
Fuel consumption rate = 422,000 gallons / 8,964 miles ≈ 47.08 gallons/mile (approximate value)
3. Since the flight time is given in hours, we need to establish a relationship between miles and hours.
4. Assume a constant speed for the jet, we can use the formula Speed = Distance / Time to express distance in terms of speed and time.
Distance = Speed * Time
5. Rearrange the formula to express Time in terms of Distance and Speed.
Time = Distance / Speed
6. Substitute the derived fuel consumption rate (gallons/mile) for Speed and rearrange the formula to express Distance in terms of Time and Speed.
Distance = Speed * Time
7. Since the fuel consumption rate is given in gallons/mile, multiply the distance by the fuel consumption rate to obtain the amount of gasoline consumed in gallons.
Gasoline consumed = Distance * Fuel consumption rate
8. Substitute the formula for Distance (Speed * Time) into the gasoline consumed formula.
Gasoline consumed = (Speed * Time) * Fuel consumption rate
9. Simplify the equation by multiplying the constants Speed and Fuel consumption rate.
Gasoline consumed = (Speed * Fuel consumption rate) * Time
10. The term (Speed * Fuel consumption rate) represents the rate at which gasoline is consumed. Let's call it the fuel consumption rate (FCR).
Gasoline consumed = FCR * Time
11. Therefore, the linear model representing the amount of gasoline on the plane, in gallons, as a function of the flight time, in hours, is:
Gasoline = FCR * Time