A man travels a total distance of 60 km in 7 hours. He walks part of the way at 6 km/h and rides a bicycle for the remaining part at 12 km/h. What distance (in km) does he travel on foot?

Introduction / Context:
This question mixes two different speeds over different portions of a journey and gives the total distance and total time. We need to determine how much of the journey was done at each speed. This is a standard type of time and distance problem where we translate the description into simultaneous equations in terms of time or distance. Solving these equations reveals how long or how far the person travelled by each mode of transport.

Given Data / Assumptions:

Total distance = 60 km.
Total time = 7 hours.
Walking speed = 6 km/h.
Cycling speed = 12 km/h.
Let the walking time be t1 hours and the cycling time be t2 hours.
We assume speeds remain constant for each mode of travel.

Concept / Approach:
We build two equations: one from the total time and one from the total distance. The time equation is t1 + t2 = 7. The distance equation is 6 * t1 + 12 * t2 = 60. These two linear equations in t1 and t2 can be solved using substitution or elimination. Once we have t1, the walking time, we can compute walking distance as 6 * t1. This systematic algebraic approach is reliable and prevents guesswork.

Step-by-Step Solution:
Step 1: Write the time equation. t1 + t2 = 7. Step 2: Write the distance equation. 6 * t1 + 12 * t2 = 60. Step 3: Use substitution from t1 + t2 = 7, so t1 = 7 - t2. Step 4: Substitute into the distance equation. 6 * (7 - t2) + 12 * t2 = 60. 42 - 6 * t2 + 12 * t2 = 60. 42 + 6 * t2 = 60. 6 * t2 = 18, so t2 = 3 hours. Step 5: Find t1. t1 = 7 - 3 = 4 hours. Step 6: Compute walking distance. Walking distance = 6 * t1 = 6 * 4 = 24 km.

Verification / Alternative check:
Cycling distance is 12 * t2 = 12 * 3 = 36 km. Total distance = 24 + 36 = 60 km, which matches the given distance. Total time = 4 + 3 = 7 hours, also matching the given time. This confirms that the breakdown of 24 km walking and 36 km cycling is correct and that the algebraic solution is consistent with the story of the problem.

Why Other Options Are Wrong:
Option a (15 km) and option b (9 km) would require much longer cycling distances and would not sum up to 60 km with only 7 hours available at the given speeds. Option c (48 km) would leave only 12 km for cycling, which at 12 km/h takes 1 hour, making the total time 9 hours instead of 7. Only 24 km fits both the time and distance constraints simultaneously.

Common Pitfalls:
A common mistake is to assume equal time or equal distance for walking and cycling without justification. Another frequent error is to miswrite the distance equation, for example 6 + 12 equals 60, which is obviously incorrect. Always define variables clearly, write the equations step by step and double check that they accurately reflect the problem statement before solving them.

Final Answer:
The man travels 24 km on foot.