Nilu covers a certain one-way distance in 6 hours at her onward speed. While returning, her speed decreases by 2 km/h and she takes 9 hours to cover the same distance back. What was her return speed (in km/h)?

Introduction / Context:When the same distance is covered at two different speeds, distance equality lets us equate speed×time for each leg. The speed drop and the longer return time together determine the original and return speeds.

Given Data / Assumptions:

• Onward time = 6 h at speed v.
• Return time = 9 h at speed v − 2.
• Distances are equal (out and back).

Concept / Approach:Set v*6 = (v − 2)*9 and solve for v, then compute the return speed v − 2.

Step-by-Step Solution:

Verification / Alternative check:Distances: 6×6 = 36 km outward; 9×4 = 36 km return—consistent.

Why Other Options Are Wrong:2 or 5 km/h breaks the equality 6v = 9(v − 2); 7 and 6 km/h also fail the equation.

Common Pitfalls:Using 2 km/h as the absolute return speed instead of the decrement; not ensuring both legs’ distances match.

Final Answer:4 km/h