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# Question 6

A person, rowing at the rate of 5 km/h in still water, takes thrice as much time in going 40 km upstream as in going 40 km downstream. Find the speed of the stream.

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Let the speed of the stream be x km/hr.

And, the speed of the boat in still water = 5 km/hr

Speed of the boat upstream = (5 – x)km/hr

Speed of the boat downstream = (5 + x) km/hr

Time taken in rowing 40 km upstream = 40/(5-x) hrs

Time taken in rowing 40 km downstream = 40/(5+x) hrs

According to the question, we have

Time taken in 40 km upstream = 3 × Time taken in 40 km downstream

\therefore \frac{40}{5-x}=\frac{3 \times 40}{5+x} \\ \Rightarrow \frac{1}{5-x}=\frac{3}{5+x} \\ \Rightarrow-3 x+15=x+5 \\ \Rightarrow-3 x-x=5-15 \\ \Rightarrow-4 x=-10 \\ \Rightarrow x=\frac{10}{4}

⇒ x = 2.5 km/hr

Hence, the speed of stream is 2.5 km/hr.

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