A boat takes a total of 3 hours to travel from place M to N downstream and then back from N to M upstream. If the boat’s speed in still water is 4 km/h, what is the distance MN? (Assume stream speed is unknown.)

Introduction / Context:
Data adequacy problems ask whether the given information uniquely determines the answer. Here, we have total round-trip time and still-water speed, but the stream speed is not provided.

Given Data / Assumptions:

• Total time T = 3 h
• Still-water speed b = 4 km/h
• Unknown current c
• Distance each way = d km

Concept / Approach:
The time equation is T = d/(b + c) + d/(b − c). Without c, multiple (d, c) pairs can satisfy the same T; therefore, d is not uniquely determined.

Step-by-Step Reasoning:

Verification / Alternative check:
Try c = 1 km/h: then 3 = d/5 + d/3 ⇒ 3 = ( (3d + 5d) / 15 ) ⇒ d = 45/8 = 5.625 km. Try c = 0.5 km/h: 3 = d/4.5 + d/3.5, leading to a different d. Hence non-unique.

Why Other Options Are Wrong:
Any specific distance assumes a particular c; since c is not given, those values are not guaranteed.

Common Pitfalls:
Assuming c = 0 or guessing c. A unique distance requires either c or one additional relation.

Final Answer:
Data inadequate.