If a person walks at 15 km/h instead of 9 km/h, he would cover 3 km more in the same time. What is the actual distance (in km) that he covers at 9 km/h?

Introduction / Context:
This question deals with comparing distances covered at two different speeds over the same time interval. The person could walk at 9 km/h but instead walks at 15 km/h and covers 3 km more in the same time. From this information we must find the actual distance he covered at the slower speed of 9 km/h. This is a typical algebraic application of the formula distance = speed * time.

Given Data / Assumptions:

• Actual intended speed = 9 km/h.
• Alternative speed = 15 km/h.
• Time of travel is the same in both cases.
• Distance at 15 km/h exceeds distance at 9 km/h by 3 km.
• We must find the distance at 9 km/h.

Concept / Approach:
Let the common time of travel be t hours. Then:
Distance at 9 km/h = 9t. Distance at 15 km/h = 15t. We know that:
15t - 9t = 3. From this we can solve for t and then compute the actual distance 9t.

Step-by-Step Solution:
Step 1: Set up the equation using the distance difference. 15t - 9t = 3. Simplify: 6t = 3. Step 2: Solve for t. t = 3 / 6 = 0.5 hours. So the person travels for half an hour. Step 3: Compute the actual distance at 9 km/h. Distance = speed * time = 9 * 0.5 = 4.5 km. Therefore, the actual distance travelled at 9 km/h is 4.5 km.
Verification / Alternative check:
At 9 km/h for 0.5 hours, the distance is 4.5 km. At 15 km/h for the same 0.5 hours, the distance is 15 * 0.5 = 7.5 km. The difference between the two is:
7.5 - 4.5 = 3 km. This matches the problem statement, so the solution is consistent and correct.

Why Other Options Are Wrong:
5.5 km or 6.5 km would require a different time t that does not make the distance difference exactly 3 km when combined with 15 km/h.
7.5 km is actually the distance at 15 km/h, not at 9 km/h.
3.5 km is too small and would not result in a 3 km difference when compared with the distance at 15 km/h over the same time.
Only 4.5 km satisfies the given condition of a 3 km extra distance at the higher speed.

Common Pitfalls:
Some learners incorrectly assume the 3 km difference applies directly to speed rather than distance. Others forget to introduce the time variable t and attempt to solve with distances alone. Misinterpreting the statement “in the same time” is also common; it is crucial because it allows us to set up the difference equation. Carefully translating the words into algebraic expressions avoids these errors.

Final Answer:
The person actually travels 4.5 km at the speed of 9 km/h.