A boatman rows 1 km in 5 minutes along the stream (downstream), and 6 km in 1 hour against the stream (upstream). Find the speed of the stream (in km/h).

Introduction / Context:This question gives downstream and upstream travel rates to deduce the current speed. Converting times to hours is essential.

Given Data / Assumptions:

• Downstream: 1 km in 5 min ⇒ 5 min = 5/60 h = 1/12 h.
• Upstream: 6 km in 1 h.
• Downstream speed vd and upstream speed vu are in km/h.

Concept / Approach:Compute vd and vu, then use vd = b + c and vu = b − c to find current c = (vd − vu)/2.

Step-by-Step Solution:

Verification / Alternative check:Then b = (vd + vu)/2 = (12 + 6)/2 = 9 km/h; check: b + c = 12 and b − c = 6, consistent with data.

Why Other Options Are Wrong:6, 10, 12 km/h do not satisfy both downstream and upstream relations simultaneously when combined with a single boat speed b.

Common Pitfalls:Forgetting to convert 5 minutes to hours; misapplying average vs half-difference. Average gives boat speed, not current speed.

Final Answer:3 km/h.