A boat travels upstream from B to A and then downstream from A back to B in a total of 3 hours. If the boat’s still-water speed is 9 km/h and the current is 3 km/h, find the distance between A and B (in km).
Aptitude
Boats and Streams
Difficulty: Easy
Choose an option
-
A4 km
-
B6 km
-
C8 km
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D12 km
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ENone of these
Answer
Correct Answer: 12 km
Explanation
Introduction / Context:Round-trip problems use different leg speeds. Knowing still-water speed and current lets us compute each leg's speed and then the distance from total time.
Given Data / Assumptions:
- b = 9 km/h (still water)
- c = 3 km/h (current)
- Upstream speed vu = b − c = 6 km/h
- Downstream speed vd = b + c = 12 km/h
- Total time = 3 h; one-way distance = d km
Concept / Approach:Total time = d/vu + d/vd. Solve for d.
Step-by-Step Solution:
3 = d/6 + d/12 = d * (1/6 + 1/12) = d * (1/4)d = 3 * 4 = 12 kmVerification / Alternative check:Upstream time = 12/6 = 2 h; downstream time = 12/12 = 1 h; total = 3 h, matches.
Why Other Options Are Wrong:4, 6, 8 give totals smaller than 3 h; they do not satisfy the time equation.
Common Pitfalls:Using the arithmetic average of speeds to find time. Average speed is not applicable across legs with different speeds unless weighted by time/distance correctly.
Final Answer:12 km.