Question : A man rows to a place 48 km distance and comes back in 14 hours. He finds that he can row 4 km with the stream at the same time as 3 km against the stream. The speed of the stream is:
Option 1: 1.5 km/h
Option 2: 3.5 km/h
Option 3: 1.8 km/h
Option 4: 1 km/h
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Correct Answer: 1 km/h
Solution : Suppose he moves 4 km downstream in $x$ hours. ⇒ Speed downstream =$\frac{4}{x}$ km/hr And, speed upstream =$\frac{3}{x}$ km/hr According to the question, $\frac{48}{\frac{4}{x}}+\frac{48}{\frac{3}{x}}=14$ ⇒ $\frac{48x}{4}+\frac{48x}{3}=14$ ⇒ $\frac{144x+192x}{12}=14$ ⇒ $336x=168$ ⇒ $x=\frac{168}{336}=\frac{1}{2}$ ⇒ Speed downstream = 8 km/hr And, speed upstream = 6 km/hr. ⇒ Speed of the stream =$\frac{1}{2}(8−6)$ km/hr = 1 km/hr Hence, the correct answer is 1 km/hr.
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