Answer:
Since we only have the weight per cubic meter (800 kg/m³), let's assume we know the total weight of the wheat Jack needs to transport and the capacity of each hopper car in kilograms. Here's the process:
### Given:
- Wheat density: 800 kg/m³
- Total weight of wheat: \(W\) kilograms
- Capacity of each hopper car: \(C\) kilograms
### Steps to Calculate the Number of Hopper Cars Needed:
1. Calculate the total volume of wheat using the total weight and density.
2. Determine how many hopper cars are needed based on their capacity.
### Formulae:
[tex]1. \(\text{Total volume of wheat} (V) = \frac{W}{800} \) cubic meters
[/tex]
[tex]2. \(\text{Number of hopper cars} = \frac{W}{C} \)[/tex]
### Example Calculation:
Assume:
- Total weight of wheat,
[tex]\(W = 16000\) kg[/tex]
- Capacity of each hopper car,
[tex]\(C = 2000\) kg[/tex]
1. Total volume of wheat:
[tex]\[
V = \frac{16000 \, \text{kg}}{800 \, \text{kg/m}^3} = 20 \, \text{m}^3
\]
[/tex]
2. Number of hopper cars needed:
[tex]\[
\text{Number of hopper cars} = \frac{16000 \, \text{kg}}{2000 \, \text{kg/car}} = 8 \, \text{cars}
\]
[/tex]
So, Jack would need 8 hopper cars to transport 16000 kg of wheat, assuming each car can carry 2000 kg.
