Time, speed and distance: If Hema walks at 12 km/h instead of 8 km/h and would then cover 20 km more in the same time, what is the actual distance (in km) that she really walked at 8 km/h?

Introduction / Context:
Questions of this type test the core relationship between speed, distance and time. When a person changes speed but walks for the same duration, the difference in distances covered directly reflects the difference in speeds. This is a standard time, speed and distance concept that appears frequently in aptitude exams.

Given Data / Assumptions:

• Actual walking speed of Hema = 8 km/h.
• Hypothetical walking speed of Hema = 12 km/h.
• Time of walking in both situations is the same.
• At the higher speed she would walk 20 km more than at the lower speed.

Concept / Approach:
We use the basic formula distance = speed * time. If the time is the same, the difference in distance is equal to the difference in speed multiplied by that common time. Once we find the time, we can compute the actual distance covered at 8 km/h.

Step-by-Step Solution:
Let the common time of walking be t hours. Distance at 8 km/h = 8 * t km. Distance at 12 km/h = 12 * t km. Given that the faster option would cover 20 km more: 12 * t - 8 * t = 20. Simplify: 4 * t = 20. So t = 20 / 4 = 5 hours. Actual distance at 8 km/h = 8 * 5 = 40 km.

Verification / Alternative check:
If Hema walked 5 hours at 8 km/h, she covers 40 km. At 12 km/h for 5 hours, she would cover 60 km. The difference is 60 - 40 = 20 km, which matches the given condition, so the solution is consistent.

Why Other Options Are Wrong:

• 32 km: Would imply a much shorter time and would not give a 20 km difference when speed is raised to 12 km/h.
• 30 km: The difference between distances at 8 km/h and 12 km/h would not be exactly 20 km.
• 46 km: Leads to a non-integer or inconsistent time value when back-calculated.

Common Pitfalls:
Candidates sometimes equate the ratio of speeds directly with the ratio of distances without considering the extra distance. Another common error is to treat 20 km as the total distance and not as the difference between the two scenarios. Forgetting that the time remains the same in both cases leads to wrong equations.

Final Answer:
The actual distance Hema walked at 8 km/h is 40 km.