When the cars are traveling in the same direction, the relative speed is the difference between their speeds. Let $u$ be the speed of the first car and $v$ be the speed of the second car.

Given:

• The distance between A and B is $100$ km.
• When traveling in the same direction, the cars meet after $S$ hours.

Since they are traveling in the same direction, the relative speed is: $|u - v|$

The distance covered by the cars before meeting when traveling in the same direction is the relative distance between them, which is $100$ km.

So, the time taken to cover this distance at the relative speed is $S$ hours.

Thus, we have: $S = \frac{100}{|u - v|}$

Rearranging for the relative speed: $|u - v| = \frac{100}{S}$

So, the relative speed of the cars when they are traveling in the same direction is: $|u - v| = \frac{100}{S}$

Would you like to know more details or have any questions?

Here are 8 related questions that can expand your understanding:

1. How can we find the individual speeds of the cars if we know the times when they travel towards and away from each other?
2. What is the relative speed of both cars while they are traveling towards each other?
3. How can the meeting point be calculated if the speeds of both cars are known?
4. What would be the effect on meeting time if one car's speed is doubled?
5. How does the concept of relative speed apply to objects moving in opposite directions?
6. How can we derive the time taken if one car is stationary and the other is moving?
7. How can we express the speed of one car in terms of the other and the given conditions?
8. What are the possible values for $u$ and $v$ if the meeting time is the same in both directions?

Tip: Always consider the direction of motion when calculating relative speeds; it can simplify understanding and solving problems involving moving objects.