Upstream speed from downstream speed and stream rate: A swimmer's downstream speed is 11 km/h and the stream's speed is 1.5 km/h. What is the swimmer's upstream speed?
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A8 km/h
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B9.5 km/h
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C9 km/h
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D6.25 km/h
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E7.5 km/h
Answer
Correct Answer: 8 km/h
Explanation
Introduction / Context:Given a downstream speed and the current, we can recover the still water speed and then compute the upstream speed. This is a standard inverse application of relative speed in a stream.
Given Data / Assumptions:
- Downstream speed u + v = 11 km/h
- Stream speed v = 1.5 km/h
- Uniform straight current
Concept / Approach:Compute u = (downstream + upstream)/2 is a known identity, but more directly with known downstream and v: u = (u + v) - v. Then upstream speed = u - v.
Step-by-Step Solution:
u + v = 11v = 1.5u = 11 - 1.5 = 9.5 km/hUpstream speed = u - v = 9.5 - 1.5 = 8 km/hVerification / Alternative check:If upstream is 8 and downstream is 11, the still water speed is (8 + 11)/2 = 9.5 km/h, which matches u above.
Why Other Options Are Wrong:
- 9.5 km/h is still water speed, not upstream.
- 9 km/h and 7.5 km/h do not satisfy the given downstream with v = 1.5.
- 6.25 km/h is unrelated to these linear sums.
Common Pitfalls:Confusing downstream value with still water speed or subtracting twice. Always compute u first, then upstream u - v.
Final Answer:8 km/h