Mixed-speed travel over fixed time A man covers 18 km in 5 hours partly walking at 2 km/h and partly running at 6 km/h. How many kilometres does he cover by running?

Introduction / Context:
We have a time split between two constant speeds. With total time and total distance known, set up linear equations in walking time and running time, then compute the running distance.

Given Data / Assumptions:

• Total time = 5 h.
• Walking speed = 2 km/h; running speed = 6 km/h.
• Total distance = 18 km.

Concept / Approach:
Let r = hours of running and w = hours of walking. Then r + w = 5 and 6r + 2w = 18. Solve for r, then compute running distance 6r.

Step-by-Step Solution:
r + w = 5 ⇒ w = 5 − r.6r + 2w = 18 ⇒ 6r + 2(5 − r) = 18 ⇒ 6r + 10 − 2r = 18.4r = 8 ⇒ r = 2 hours.Running distance = 6 × r = 12 km.

Verification / Alternative check:
Walking time = 3 h ⇒ walking distance = 2 × 3 = 6 km; total = 6 + 12 = 18 km, consistent.

Why Other Options Are Wrong:
15 km or 10 km would violate either distance or time totals; 9 km corresponds to r = 1.5 h, not meeting the 18 km total.

Common Pitfalls:
Confusing time-weighted and distance-weighted averages; forgetting that times (not distances) must sum to 5 hours.

Final Answer:
12 km