Speed of the current from contrasting paces: A boat moves upstream at 1 km in 10 minutes and downstream at 1 km in 6 minutes. What is the speed of the current?

Introduction / Context:
Given unit distances and times in each direction, convert to effective speeds and use their difference to find the stream speed. This illustrates how time per kilometer maps to speed in km/h.

Given Data / Assumptions:

• Upstream: 1 km in 10 minutes = 0.1667 h
• Downstream: 1 km in 6 minutes = 0.1 h
• Uniform current

Concept / Approach:
Compute su and sd, then v = (sd - su)/2. Keep units consistent by converting minutes to hours before inversion.

Step-by-Step Solution:

Verification / Alternative check:
The still water speed u = (sd + su)/2 = (10 + 6)/2 = 8 km/h. Then u ± v = 8 ± 2 gives 10 and 6, matching inputs.

Why Other Options Are Wrong:

• 1.5 km/h and 1 km/h underestimate the current given the large directional difference.
• 2.5 km/h and 3 km/h overshoot the needed difference of 4 km/h between sd and su.

Common Pitfalls:
Failing to convert minutes to hours; averaging times rather than speeds. Speed is distance divided by time in hours here.

Final Answer:
2 km/h