A person walks at 12 km/h instead of 10 km/h and would then cover 1 kilometre more in the same time. What is the actual distance in kilometres that he walks at 10 km/h in that time?

Introduction / Context:

This problem is another example of how changing speed while keeping time constant affects the distance travelled. It states that if the person walks faster, he covers 1 kilometre more in the same time. From this information we must find the actual distance he covers at the lower speed. Such questions are important for building algebraic thinking using the basic speed, time and distance formula.

Given Data / Assumptions:

• Lower walking speed = 10 km/h.
• Higher walking speed = 12 km/h.
• The time of travel is the same in both cases.
• At the higher speed he covers 1 km more than at the lower speed.
• We must find the distance covered at 10 km/h.

Concept / Approach:

Using distance = speed * time, we express the distance at each speed in terms of a common time variable. The difference between these distances is given as 1 km. This yields a simple linear equation in the time variable. Once we find the time, we can compute the distance covered at 10 km/h. This algebraic method avoids guesswork and works systematically for all similar problems.

Step-by-Step Solution:

Verification / Alternative check:

We can verify numerically. If t = 0.5 hours, distance at 10 km/h is 10 * 0.5 = 5 km. Distance at 12 km/h is 12 * 0.5 = 6 km. The difference is 6 - 5 = 1 km, which matches exactly the condition in the question. Therefore t and the distance at 10 km/h are correctly calculated, and 5 km is the required answer.

Why Other Options Are Wrong:

If the distance were 8 km at 10 km/h, the time would be 8 / 10 = 0.8 hours and at 12 km/h the distance would be 9.6 km, giving a difference of 1.6 km, not 1 km. Similarly, if the distance were 10 km, the difference between 12t and 10t would not be 1 km. A distance of 12 km would imply an even larger difference. Only a distance of 5 km leads to exactly a 1 km increase when the speed rises from 10 to 12 km/h.

Common Pitfalls:

One common mistake is to assume that 2 km/h extra speed directly adds 2 km to the distance, which is not true because time also matters. Others attempt to guess the distance instead of forming an equation, leading to confusion. Some learners also forget that the time is the same in both cases and try to set up two separate unrelated expressions.

Final Answer:

The person actually walks 5 kilometres at 10 km/h in that time.