Question

6. A plane due to fly from Montreal to Edmonton required refueling. Because the fuel gauge on the aircraft was not working, a mechanic used a dipstick to determine that 7682 L of fuel were left on the plane. The plane required 22,300 kg of fuel to make the trip. In order to determine the volume of fuel required during the refueling, the pilot asked for the density of the fuel so he could convert a volume of fuel to a mass of fuel. The mechanic provided a factor of 1.77. Assuming that this factor was in metric units (kg/L), the pilot calculated the volume to be added as 4916 L. This volume of fuel was added and the plane subsequently ran out of fuel, but landed safely by gliding into Gimli Airport near Winnipeg. The error arose because the factor 1.77 was in units of pounds per liter (lbs/L). How many liters of fuel should have been added

Answer 1

Answer:

The amount of liters of fuel should have been added is  20093 L

Explanation:

Given that;

a mechanic used a dipstick to determine that 7682 L of fuel were left on the plane

i.e the volume of fuel left in the plane = 7682 L

Required fuel to make  a trip = 22,300 kg of fuel

Also from the question; we are being told that in order for the pilot to determine the volume ; he asked for the density of the fuel and the mechanic said 1.77.

This volume of fuel was added and the plane subsequently ran out of fuel, but landed safely by gliding into Gimli Airport near Winnipeg. The error arose because the factor 1.77 was in units of pounds per liter (lbs/L).

Now; we can understand that the density of the fuel was 1.77 pound /litre.

SO , let convert 1.77 pound /litre to kg/Litre;

we all know that

1 pound = 0.4536 kg

1.77 pound/litre  = x kg

If we cross multiply ; we will have:

1.77 pound/litre  × 0.4536 kg = 1 pound × x kg

x kg = (1.77 pound/litre  × 0.4536 kg) /1 pound

x = 0.802872 kg/litre

$\mathbf{Density = \dfrac{mass}{volume}}$

where ;

mass =  22,300 kg of fuel

volume = unknown ???

density = 0.802872 kg/litre

making volume the subject of the formula from above; we have:

$\mathbf{volume = \dfrac{mass}{Density}}$

$\mathbf{volume = 22300 \ kg \ of \ fuel *\dfrac{1 \ litre }{0.802872 \ kg \ of \ fuel}}$

volume = 27775.28672 litre

volume $\approx$ 27775 L

Let not forget that we are being told as well that the volume of fuel left in the plane = 7682 L

Now;

The amount of liters of fuel should have been added is: =  27775 L - 7682 L

The amount of liters of fuel should have been added is  20093 L