Question : A man rows from J to K (upstream) and back from K to J (downstream) in a total time of 15 hours. The distance between J and K is 300 km. The time taken by the man to row 9 km downstream is identical to the time taken by him to row 3 km upstream. What is the approximate speed of the boat in still water?
Option 1: 51.33 km/hr
Option 2: 47.67 km/hr
Option 3: 53.33 km/hr
Option 4: 43.67 km/hr
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Correct Answer: 53.33 km/hr
Solution : Let the speed of the boat as B and the speed of the stream as S. Upstream Speed = B – S Downstream Speed = B + S ⇒ A man rows from J to K (upstream) and back from K to J(downstream) in a total time of 15 hours. The distance between J and K is 300 km. According to the question, $\frac{300}{B + S}$ + $\frac{300}{B – S}$ = 15 ⇒ $\frac{20}{B + S}$ + $\frac{20}{B – S}$ = 1 Since the time taken by him to row 3 km upstream is equal to the time taken by him to row 9 km downstream. So, $\frac{9}{B + S}$ = $\frac{3}{B – S}$ ⇒ $\frac{B + S}{B - S}$ = $\frac{3}{1}$ From this, we can take the speed of the boat as B = 2$x$ km/hr, and the speed of the stream as S = $x$ km/hr So, $\frac{20}{ 2x + x} + \frac{20}{2x – x}=1$ ⇒ $\frac{20}{ 3x } + \frac{20}{x}=1$ ⇒ $x = \frac{80}{3}$ So, the speed of boat in still water, B = 2$x$ km/hr = 2 × $\frac{80}{3}$ = 53.33 km/hr Hence, the correct answer is 53.33 km/hr.
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