Two cars start from a common point. The $1^{\text{st}}$ car travels north $10\text{km}$, turns left and goes ahead for $8\text{km}$. The $2^{\text{nd}}$ car goes south for $5\text{km}$, turns right and travels $8\text{km}$. What is the distance between the cars?

Let's trace the positions relative to the starting point $(0,0)$:
1. Car 1: Goes North $10\text{km}\to (0,10)$. Turns left (West) and goes $8\text{km}\to (-8,10)$.
2. Car 2: Goes South $5\text{km}\to (0,-5)$. Turns right (West, since facing South) and goes $8\text{km}\to (-8,-5)$.

Both cars are at the same longitudinal alignment ($x=-8$). The distance between them is the vertical difference in their coordinates:

$$\text{Distance}=10-(-5)=10+5=15\text{km}$$