School commute — late vs early times at 4 km/h and 6 km/h: A student walking at 4 km/h reaches school 10 min late. Next day, walking at 6 km/h, he reaches 5 min early. What is the distance between home and school?

Introduction / Context:
Two commute times around the schedule allow solving for distance using speed-time relationships and arrival offsets.

Given Data / Assumptions:

• At 4 km/h: arrives 10 min late ⇒ actual time = T_s + 10/60 h
• At 6 km/h: arrives 5 min early ⇒ actual time = T_s − 5/60 h
• Distance = d (km)

Concept / Approach:
d/4 − d/6 = (10 + 5)/60 h = 1/4 h.

Step-by-Step Solution:

Verification / Alternative check:
Compute schedule time T_s from either condition; both yield consistent T_s.

Why Other Options Are Wrong:
2, 4, 5, 2.5 km do not satisfy the offset equation.

Common Pitfalls:
Mixing up which arrival is late vs early or converting minutes to hours incorrectly.

Final Answer:
3 km