A boat must travel upstream 20 km from point X to point Y and return from Y to X. The total time given is 41 minutes 40 seconds. Can the speed of the boat be determined? Choose the correct option.

Difficulty: Medium

Correct Answer: Cannot be determined

Explanation:


Introduction / Context:
The statement provides a very small total time (41 min 40 s ≈ 0.694 h) for a 40 km round trip against and with current, without specifying still-water speed or current. We must evaluate if a unique answer exists.


Given Data / Assumptions:

  • Upstream distance = 20 km; downstream distance = 20 km
  • Total time T = 41 min 40 s = 41 + 40/60 min = 41.666... min ≈ 0.694 h
  • Unknown still-water speed b and current c


Concept / Approach:
The time equation T = 20/(b − c) + 20/(b + c) has infinitely many (b, c) solutions for a fixed T unless additional constraints are given. Moreover, the given T seems unrealistically small for such a journey unless speeds are very high; still, with no b or c provided, there is no unique solution.


Step-by-Step Reasoning:

0.694 ≈ 20/(b − c) + 20/(b + c)Multiple pairs (b, c) > 0 can satisfy this equation; without more information, the boat’s specific speed cannot be fixed.


Verification / Alternative check:
Trial values of b and c can be found to approximate the total, but uniqueness is absent. Also, the options list specific speeds without context; none can be uniquely justified.


Why Other Options Are Wrong:
66, 72, or 48 km/h cannot be deduced from the data and would be arbitrary picks.


Common Pitfalls:
Assuming still water (c = 0) or guessing current; the problem provides neither, so the answer is indeterminate.


Final Answer:
Cannot be determined.

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