Question : A man rows to a place 35 km in distance and back in 10 hours 30 minutes. He found that he could row 5 km with the stream at the same time as he could row 4 km against the stream. Find the rate of flow of the stream:
Option 1: 1 km/hr
Option 2: 0.5 km/hr
Option 3: 0.75 km/hr
Option 4: 1.5 km/hr
Correct Answer: 0.75 km/hr
Solution :
Given: Time taken to row 5 km with the stream = Time taken to row 4 km against the stream.
Also, the time taken to row 35 km and back = 10 hours 30 minutes
Let the speed of man and stream be $V, U$, respectively.
$\frac{5}{(V+U)}=\frac{4}{(V−U)}$ . . . . . . (travelling distance in same time)
$⇒5V-5U=4V+4U$
$⇒V=9U$
$⇒\frac{V}{U}=\frac{9}{1}$
Let $U=x, V=9x$
Also, $\frac{35}{2}(\frac{1}{(U+V)}+\frac{1}{(U-V)})=\frac{21}{2}$
$⇒\frac{35}{2x}(\frac{1}{5}+\frac{1}{4})=\frac{21}{2}$
$⇒\frac{5}{x}\times \frac{9}{20}=3$
$\therefore x=\frac{3}{4}=0.75$
Speed of stream = $1\times0.75$ = 0.75 km/hr
Hence, the correct answer is 0.75 km/hr.
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