Uniform speed scaling A man cycles 12 km in 90 minutes at a uniform speed. How far will he travel in 3 hours at the same speed?

Introduction / Context:
When speed is uniform, distance is directly proportional to time. Doubling the time doubles the distance; tripling the time triples the distance, and so on.

Given Data / Assumptions:

• Covers 12 km in 90 minutes.
• Required time = 3 hours = 180 minutes.
• Speed remains constant throughout.

Concept / Approach:
Compute speed first, then multiply by the new time. Speed (km/h) = distance / time.

Step-by-Step Solution:

Verification / Alternative check:
Proportion method: 180 min is twice 90 min, so distance doubles from 12 km to 24 km.

Why Other Options Are Wrong:
27 km (needs 3.375 h at 8 km/h), 30 km (needs 3.75 h), 36 km (needs 4.5 h).

Common Pitfalls:
Mixing minutes and hours without converting consistently.

Final Answer:
24 km