Step 1: Understanding the Concept:
This problem deals with uniform or constant speed. When an object moves at a constant speed, the distance it travels is directly proportional to the time taken. This means that if you double the time, the distance traveled will also double. We can solve this by first finding the uniform speed of the car per hour (unitary method) and then using that speed to find the total distance for the new time duration.
Step 2: Key Formula or Approach:
The fundamental relationship between speed, distance, and time is given by:
$$ \text{Speed } (v) = \frac{\text{Distance } (d)}{\text{Time } (t)} $$
Rearranging this formula to find distance gives:
$$ \text{Distance } (d) = \text{Speed } (v) \times \text{Time } (t) $$
Step 3: Detailed Explanation:
Let's break the calculation down into two simple parts:
1. Find the constant speed of the car:
We are given that the car covers a distance of $240 \text{ km}$ in $4 \text{ hours}$.
$$ v = \frac{240 \text{ km}}{4 \text{ hours}} = 60 \text{ km/h} $$
This tells us the car travels exactly $60 \text{ km}$ during every single hour of its journey.
2. Calculate the distance covered in 7 hours:
Since the car continues driving at this exact same speed ($v = 60 \text{ km/h}$), we multiply it by the new time duration ($t = 7 \text{ hours}$):
$$ d = 60 \text{ km/h} \times 7 \text{ hours} $$
$$ d = 420 \text{ km} $$
This calculated value matches option (C).
Step 4: Final Answer:
The distance the car will cover in 7 hours is 420 km, which corresponds to option (C).