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 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.
Use a linear model to predict the amount of gasoline that is present on the Jet after it has been in flight for 18 hours without stopping to refuel. In two or more complete sentences, explain your answer.

Answer 1

78 miles

Explanation:

Answer 2

plane is consuming 26375 gallons per hour.

plane is consuming 29.24462924 gallons per kilometer.

plane is traveling at 901.875 kilometers per hour.

the plane has a capacity of 422000 gallons of gas.

the plane can travel 14430 kilometers on this amount of fuel.

the plane uses 52750 gallons of gas every 2 hours.

divide that by 2 to get 52750 / 2 = 26375 gallons of gas per hour.

take the 422000 gallons and divide it by 14430 kilometers to get 422000 / 14430 = 29.24462924 gallons of gas consumed per kilometer.

take the 422000 gallons of gas and divide it by 26375 to get 422000 / 26375 = 16 hours.

the plane can travel 14430 kilometers in 16 hours, therefore the plane must be flying at 14430 / 16 = 901.875 kilometers per hour.

now I tried figuring how many gallons equals a kilometer which I know that 1 gallon = 4 Liters and 1 Liter = 23,860 gallons is 4 liters 13.5/hr = 48,600 gallons but the rest I can't figure from the

1 gallon equals 4 quarts, not 4 liters.

1 quart equals 0.946353 liters

therefore 1 gallon equals 4 * .946353 = 3.785412 liters.

in any case, you didn't need to do any of those conversions since you wanted gallons per kilometer and you could calculate that directly from the information that was given to you.

calculating the average speed of the plane was a little trickier.

you know that the plane is using 26375 gallons per hour.

you know that the plane is using 29.24462924 gallons per kilometer.

divide 26375 gallons per hour by 29.24462924 gallons per kilometer and you get 26375 / 29.24462924 = 901.875 kilometers per hour.

how does that work?

let g = gallons and k = kilometers and h = hours.

26375 is gallons per hour = g/h

29.24462924 is gallons per kilometer = g/k

26375 / 29.24462924 is (g/h) / (g/k).

this is equivalent to (g/h) * (k/g)

the g in the numerator and denominator cancel out and you are left with:

(k/h) which is kilometers per hour.

plane is consuming 26375 gallons per hour.

plane is consuming 29.24462924 gallons per kilometer.

plane is traveling at 901.875 kilometers per hour.

fyi, since there are 0.621371 miles per kilometer, then the plane is traveling at 560.3989706 miles per hour which is quite reasonable based on the capability of that plane.

if you want to know how much fuel is left on the plane after x hours of flying, then the equation for that would be:

y = 422000 - 26375 * x