A man rows to a place 48 km away and returns in a total of 14 hours. He can row 4 km with the stream in the same time as 3 km against it. What is the stream's speed?

Given data

• Out-and-back distance: 48 km each way
• Total time = 14 h
• Time to row 4 km downstream equals time to row 3 km upstream ⇒ 4/(u + v) = 3/(u − v)

Concept / Approach

• From 4/(u + v) = 3/(u − v), deduce relation between u and v.
• Use round-trip time formula: T = 48/(u + v) + 48/(u − v).

Step-by-step calculation

4(u − v) = 3(u + v) ⇒ 4u − 4v = 3u + 3v ⇒ u = 7vTotal time T = 48/(u + v) + 48/(u − v) = 96u/(u^2 − v^2)With u = 7v: u^2 − v^2 = 49v^2 − v^2 = 48v^2T = 96·7v / (48v^2) = 14 / vSet T = 14 ⇒ 14/v = 14 ⇒ v = 1 km/h

Verification

u = 7 km/h; downstream = 8 km/h; upstream = 6 km/h; times: 48/8 + 48/6 = 6 + 8 = 14 h.

Common pitfalls

• Assuming arithmetic average of speeds instead of using the given time ratio.

Final Answer

1 km/h