Mixed-mode travel — 50 km in 8 h with walking and cycling: A person covers 50 km in 8 h by walking at 4 km/h for some distance and cycling at 10 km/h for the remainder. How many kilometres did he walk?

Introduction / Context:This is a standard two-mode mixture problem with fixed total distance and time.

Given Data / Assumptions:

• Total distance = 50 km; total time = 8 h
• Walking speed = 4 km/h; cycling speed = 10 km/h
• Let walking distance = x ⇒ cycling distance = 50 − x

Concept / Approach:Total time x/4 + (50 − x)/10 = 8. Solve for x.

Step-by-Step Solution:

Verification / Alternative check:Time check: 20/4 = 5 h; (30)/10 = 3 h ⇒ total 8 h.

Why Other Options Are Wrong:They do not satisfy the time equation.

Common Pitfalls:Assuming equal time in both modes; the time split depends on distances and speeds.

Final Answer:20 km