Question 1087420: 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. O hours full fuel 422,000 gallons Every 2 hours uses 52,750 gallons.
I did the y = mx-b formula to get the average of 52,750 from a graph
which won't copy onto here. but it went like this
(0,422,000) (1, 369, 250) 422,000 - 369, 250 over 0-1 = 52,750/1=52,750
(2, 316,500) (3, 263,750) 315,500-263,750/3-2=52,750-1=52,750 (4, 211,000) (5, 158,250) 211,000-158,250/5-4=52,750/1=52,750 and (6, 105,500) (7, 52,750) 105,500-52,750/7-6=53,750/1=52,750
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 word problem that I don't understand and need help in figuring it
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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.
looks like you got lost here:
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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 word problem that I don't understand and need help in figuring it.
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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.
bottom line is:
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
y represents the fuel left on the plane.
x represents the number of hours the plane is flying.
graphically, this would look like this:
if you want to know how much fuel is left on the plane after x kilometers of flying, then the equation for that would be:
y = 422000 - 29.24462924 * x
y represents the fuel left on the plane.
x represents the number of kilometers the plane is flying.
graphically, this would look like this:
if you want to know how many kilometers are left after x hours of flying, then the equation for that would be:
y = 14430 - 901.875 * x
y represents the number of flying hours left.
x represents the number of hours.
graphically, this would look like this:
if you want to know how many hours of flying the plane has left after x kilometers of flying, then the equation for that would be:
y = 16 - 16/422000 * x
y represents the number of hours of flying tine left.
x represents the number of kilometers.
graphically, this would look like this:
let me know if you're still confused about this, and if so, what you are confused about.
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