Let's break down the problem and assign variables to represent the unknowns:

Let:

• $x$ be the space (in meters) occupied by a passenger car.
• $x + 18$ be the space (in meters) occupied by a truck (since a truck takes up 18 meters more space than a car).

Now, let's calculate the total space occupied by the vehicles in both lanes.

Left Lane:

• 16 trucks: The total space taken by the trucks in the left lane is $16 \times (x + 18)$.
• 210 cars: The total space taken by the cars in the left lane is $210 \times x$.

The total space in the left lane is: $16(x + 18) + 210x$

Right Lane:

• 1 truck: The total space taken by the truck in the right lane is $1 \times (x + 18)$.
• 270 cars: The total space taken by the cars in the right lane is $270 \times x$.

The total space in the right lane is: $1(x + 18) + 270x$

Total Space:

The total space taken by all vehicles in both lanes is the sum of the total space in the left and right lanes: [ \text{Total Space} = \left[ 16(x + 18) + 210x \right] + \left[ 1(x + 18) + 270x \right] ]

Let's simplify this expression:

$\text{Total Space} = 16(x + 18) + 210x + 1(x + 18) + 270x$ $= 16x + 288 + 210x + x + 18 + 270x$ $= (16x + 210x + x + 270x) + (288 + 18)$ $= 497x + 306$

This is the total space in meters.

We now need to solve for $x$, the space occupied by a car. To do this, we would need additional information, like the total space occupied by the vehicles in both lanes. Without that information, we can express the total space in terms of $x$.

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To summarize the answer:

• a) The space a truck takes is $x + 18$ meters.
• b) The space a passenger car takes is $x$ meters.
• c) The total space occupied is $497x + 306$ meters, but we need more information to solve for $x$ directly.

Would you like me to proceed with additional details or assumptions? Let me know if you have any specific numbers for the total space, or if you'd like me to clarify any part!

Here are some related questions:

1. How would you calculate the total space if we had the total space occupied by vehicles?
2. What would happen if we had more trucks in the right lane?
3. How could you express this problem as a system of equations for different values of $x$?
4. What does it mean if the total space from both lanes is not consistent with the truck/car ratio?
5. How does this type of problem relate to real-world scenarios in transportation planning?

Tip: Try checking if the total space occupied by the vehicles in both lanes is given to solve for $x$ directly.