A boatman takes twice as long to row a fixed distance against the stream as he takes with the stream. Find the ratio of the boat speed in still water to the stream speed.

Introduction / Context:Ratio questions in boats and streams often come from time comparisons for equal distances. Because time equals distance divided by speed, a factor-of-two time difference means a specific ratio between the effective speeds, which in turn constrains the relation between the still-water speed and the current.

Given Data / Assumptions:

• D/(v − c) = 2 * D/(v + c) for the same distance D.
• v is still-water speed; c is current speed.
• No pauses; steady speeds.

Concept / Approach:Cancel D to get (v + c) = 2(v − c). Solve for v in terms of c and then express the ratio v : c.

Step-by-Step Solution:

Verification / Alternative check:Pick v = 3 and c = 1 (same units). Then downstream speed = 4, upstream speed = 2. For the same D, downstream time is D/4 and upstream time is D/2, which is exactly double.

Why Other Options Are Wrong:2:1, 1:2, 1:3 do not satisfy v = 3c and will not produce a twofold time difference for equal distances.

Common Pitfalls:Taking 2:1 between speeds instead of times; remember that time ratios invert speed ratios for the same distance.

Final Answer:3 : 1