To solve this problem, we'll calculate the amount of fuel in kilograms already present in the tanks, subtract it from the total fuel requirement, and then convert the remaining amount into liters.

Step 1: Calculate the mass of the fuel already in the tanks

Given:

• $7,682$ liters of fuel
• The mass of one liter of fuel is $0.803$ kilograms

The mass of the fuel already in the tanks is calculated as follows:

$\text{Mass of fuel in tanks} = 7,682 \times 0.803 = 6,167.846 \text{ kilograms}$

Step 2: Calculate the additional fuel required in kilograms

The total fuel requirement for the trip is $22,300$ kilograms. The additional fuel needed is:

$\text{Additional fuel required} = 22,300 - 6,167.846 = 16,132.154 \text{ kilograms}$

Step 3: Convert the additional fuel requirement from kilograms to liters

We know that $1$ liter of jet fuel has a mass of $0.803$ kilograms, so the required fuel in liters is:

$\text{Additional fuel in liters} = \frac{16,132.154}{0.803} \approx 20,088.8 \text{ liters}$

Step 4: Round the answer to the nearest whole liter

Rounding $20,088.8$ liters to the nearest whole number gives:

$\text{Additional fuel needed} = 20,089 \text{ liters}$

Final Answer

The amount of fuel that needs to be added is 20,089 liters.

Would you like to go over any part of this solution in more detail?

Here are 5 related questions for further practice:

1. How would the calculations change if the mass of one liter of jet fuel was 0.800 kilograms?
2. If the initial amount of fuel in the tank was incorrectly recorded as 7,000 liters, how much additional fuel would be needed?
3. Suppose the fuel requirement was calculated in pounds instead of kilograms. How would you convert the final answer?
4. What if the flight required 25,000 kilograms of fuel instead of 22,300 kilograms?
5. If the pilot mistakenly used the density of another type of fuel (0.820 kg/liter), what would have been the error in fuel calculation?

Tip: Always double-check unit conversions, especially in critical calculations like fuel requirements!