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Mathematics

A boatman rowing at the rate of 5 km/hr in still water takes thrice as much time in going 40 km upstream as in going 40 km downstream. What is the speed of the stream?

Linear Equations

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Answer

Let x be speed of the stream.

Given,

Speed of boat in still water = 5 km/hr.

Speed of boat in upstream = (5 - x) km/hr

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

By formula,

Time = DistanceSpeed\dfrac{\text{Distance}}{\text{Speed}}

Given,

The boatman takes thrice as much time in going 40 km upstream as in going 40 km downstream.

∴405−x=3×405+x⇒15−x=15+x⇒5+x=3(5−x)⇒5+x=15−3x⇒x+3x=15−3⇒4x=10⇒x=104⇒x=2.5 km/hr \therefore \dfrac{40}{5 - x} = 3 \times \dfrac{40}{5 + x} \\[1em] \Rightarrow \dfrac{1}{5 - x} = \dfrac{1}{5 + x} \\[1em] \Rightarrow 5 + x = 3(5 - x) \\[1em] \Rightarrow 5 + x = 15 - 3x \\[1em] \Rightarrow x + 3x = 15 - 3 \\[1em] \Rightarrow 4x = 10 \\[1em] \Rightarrow x = \dfrac{10}{4} \\[1em] \Rightarrow x = 2.5 \text{ km/hr }

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

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