A person covers 100 km in 10 hours, partly walking at 7 km/h and the rest running at 12 km/h. Find the distance covered walking and the distance covered running.

Introduction / Context:
The traveler uses two constant speeds over a fixed total time and distance. Let walking time be t hours, so running time is 10 − t. Form a single linear equation in t using distance = speed * time.

Given Data / Assumptions:

• Total time = 10 hours.
• Walking speed = 7 km/h.
• Running speed = 12 km/h.
• Total distance = 100 km.

Concept / Approach:
Total distance = 7t + 12(10 − t). Solve for t, then compute each distance separately: 7t for walking and 12(10 − t) for running.

Step-by-Step Solution:
7t + 12(10 − t) = 1007t + 120 − 12t = 100 ⇒ −5t = −20 ⇒ t = 4 hoursWalking distance = 7*4 = 28 kmRunning distance = 12*(10 − 4) = 72 km

Verification / Alternative check:
Average speed check: total distance/time = 100/10 = 10 km/h. Weighted speeds (7 for 4 h and 12 for 6 h) produce overall 10 km/h, consistent.

Why Other Options Are Wrong:
They do not satisfy both the time and distance equations simultaneously.

Common Pitfalls:
Setting up two unknown distances without relating them through time, or assuming equal times at each speed.

Final Answer:
Walking = 28 km, Running = 72 km