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 rate of the stream (in km/h).

Introduction / Context:Equal-time statements over different distances give a ratio of downstream to upstream speeds. Combine that with round-trip time to deduce the current speed.

Given Data / Assumptions:

• One-way distance d = 48 km
• Total time = 14 h
• 4 km downstream takes the same time as 3 km upstream ⇒ vd / vu = 4 / 3
• Let b be still-water speed and c the current

Concept / Approach:From vd/vu = (b + c)/(b − c) = 4/3 ⇒ b = 7c. Then use time equation d/(b − c) + d/(b + c) = 14 to find c.

Step-by-Step Solution:

Verification / Alternative check:b = 7 km/h; times: upstream 48/6 = 8 h; downstream 48/8 = 6 h; total 14 h. Ratio check: vd/vu = 8/6 = 4/3, satisfied.

Why Other Options Are Wrong:Other values for c break either the 14 h total or the 4:3 time equivalence ratio.

Common Pitfalls:Treating 4:3 as a distance ratio; it is a speed ratio because times are equal. Always convert such statements into a speed ratio relation.

Final Answer:1 km/hr.