Question 474939: An airplane has a total mass at take-off of 94 000 kg. The fuel and crew are 1/4 of the mass of the unloaded plane and the passengers and luggage are 1/3 of the mass of the fuel and crew. What is the mass of the unloaded plane.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! mass at takeoff is 94,000 kg.
this includes fuel and crew and passengers and luggage
the fuel and crew are 1/4 of the mass of the unloaded plane.
the passengers and luggage are 1/3of the mass of the fuel and crew.
let a = mass of unloaded plane.
let b = mass of fuel and crew.
let c = mass of passenters and luggage.
mass of the plane at takeoff is equal to a + b + c.
this means that:
a + b + c = 94,000 kg.
b is equal to 1/4 * a.
c is equal to 1/3 * b.
substituting for c in the equation gets:
a + b + (b/3) = 94,000 kg
substituting for b in the equation gets:
a + (a/4) + ((a/4)/3) = 94,000 kg
simplify this to get:
a + (a/4) + (a/12) = 94,000 kg
convert all denominators on the left hand side of this equation to 12 to get:
12a/12 + 3a/12 + a/12 = 94,000 kg.
combine like terms to get:
16a/12 = 94,000 kg
multiply both sides of this equation by (12/16) to get:
a = (94,000 * 12)/16 = 70,500 kg.
since b = a/4, this means that b = 70,500 / 4 = 17,625 kg.
since c = b/3, this means that c = 5,875 kg.
the sum of a + b + c = 70,500 + 17625 + 5,875 = 94,000.
the numbers look good.
we'll confirm by tracing back to the original requirements using them.
the load of the plan at takeoff is 94,000 kg.
the weight of the empty plane is equal to 70,500 kg.
the weight of the fuel and crew is equal to 1/4 of that (70,500 / 4 = 17,625 kg).
the weight of the passengers and luggage is equal to 1/3 of the weight of the fuel and crew (17,625 / 3 = 5,875).
the weight of the plane at takeoff is the weight of the unloaded plan plus the weight of the fuel and crew plus the weight of the passengers and luggage.
the weight of the plane at takeoff is equal to 70,500 + 17,625 + 5,875 which is equal to 94,000 kg.
numbers are good.
problem is solved.
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