Answer :
The mass of the unloaded plane is 70500 kg.
Let's denote the mass of the unloaded plane as P.
Given that the fuel and crew are 1/4 of the mass of the unloaded plane, we can express their combined mass as (1/4)P.
Additionally, the passengers and luggage are 1/3 the mass of the fuel and crew, so their combined mass can be represented as (1/3)(1/4)P.
Now, let's calculate the total mass at take-off:
Total mass at take-off = Mass of unloaded plane + Fuel and crew + Passengers and luggage
Since the fuel and crew are 1/4 of the unloaded plane's mass, we have:
Fuel and crew = (1/4)P
Similarly, the passengers and luggage are 1/3 of the fuel and crew's mass, so we have:
Passengers and luggage = (1/3)(1/4)P
= (1/12)P
Now, we can calculate the total mass at take-off:
Total mass at take-off = P + (1/4)P + (1/12)P
Combining like terms:
Total mass at take-off = (12/12)P + (3/12)P + (1/12)P
Total mass at take-off = (16/12)P
Given that the total mass at take-off is 94000 kg, we can set up the equation:
(16/12)P = 94000
To solve for P, we multiply both sides by (12/16):
P = (94000 × 12) / 16
P = 70500 kg
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