Planned mix of walking and cycling — total 80 km in 8 h: A man must cover 80 km in 8 h, partly on foot at 8 km/h and partly by bicycle at 16 km/h. How many kilometres should he walk?

Introduction / Context:Blend problems fix total distance and total time while two modes have different speeds. Let one distance be the variable and solve.

Given Data / Assumptions:

• Total distance = 80 km, total time = 8 h
• Walking speed = 8 km/h, cycling speed = 16 km/h
• Let walking distance = w ⇒ cycling distance = 80 − w.

Concept / Approach:Total time = w/8 + (80 − w)/16 = 8. Solve for w.

Step-by-Step Solution:

Verification / Alternative check:Check time: 48/8 = 6 h walking, 32/16 = 2 h cycling ⇒ total 8 h.

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

Common Pitfalls:Assuming time splits equally; it depends on speeds.

Final Answer:48 km