A man rows to a place 48 km away and returns in a total of 14 hours. He finds that he can row 4 km with the stream in the same time as 3 km against the stream. Find the speed of the stream.

Introduction / Context:Relating equal times for unequal distances with and against the stream gives a ratio of effective speeds, which we can use with the total round-trip time to compute the current speed.

Given Data / Assumptions:

• Distance one way = 48 km; total time = 14 h.
• Time for 4 km downstream equals time for 3 km upstream ⇒ vd : vu = 4 : 3, where vd = b + c and vu = b - c.

Concept / Approach:Let vu = 3k and vd = 4k. Then the total time is 48/(3k) + 48/(4k) = 16/k + 12/k = 28/k. Set 28/k = 14 to get k, then compute c from (vd - vu)/2.

Step-by-Step Solution: 28/k = 14 ⇒ k = 2 vu = 3k = 6 km/h; vd = 4k = 8 km/h c = (vd - vu)/2 = (8 - 6)/2 = 1 km/h

Verification / Alternative check:Round-trip time = 48/6 + 48/8 = 8 + 6 = 14 h, as given. The 4 km vs 3 km equal-time condition also holds with speeds 8 and 6 km/h.

Why Other Options Are Wrong:2, 1.5, or 2.5 km/h do not produce both the correct round-trip sum and the 4:3 speed ratio simultaneously.

Common Pitfalls:Assuming 4:3 is b:c instead of downstream:upstream; forgetting that times add over legs, not speeds; arithmetic slips in solving for k.

Final Answer:1 km/hr