A man takes twice as long to row a distance against the stream as with the stream. What is the ratio of the boat's still-water speed to the stream's speed?

Given data

• For the same distance, time upstream is twice time downstream.

Concept / Approach

• Time ratio equals inverse speed ratio for equal distances.
• If u is still-water speed and v is stream speed: (u + v) / (u − v) = 2.

Step-by-step calculation

(u + v)/(u − v) = 2 ⇒ u + v = 2u − 2vRearrange ⇒ u = 3vThus, u : v = 3 : 1

Verification

Take v = 1, u = 3 ⇒ speeds: downstream 4, upstream 2 ⇒ time ratio upstream:downstream = 4:2 = 2:1.

Common pitfalls

• Inverting the ratio leading to u = v, which contradicts the time relation.

Final Answer

3 : 1