Let x represent speed of kayak in the still water.
We have been given that a kayaker paddles 2 km upstream in the same time that it takes to paddle 3 km downstream. The average speed of the current is 1 km/h.
Speed of kayak upstream would be speed of kayak in still water minus speed of the current that is [tex]x-1[/tex].
Speed of kayak downstream would be speed of kayak in still water plus speed of the current that is [tex]x+1[/tex].
[tex]\text{Time}=\frac{\text{Distance}}{\text{Speed}}[/tex]
Time taken to travel 2 km upstream would be [tex]\frac{2}{x-1}[/tex].
Time taken to travel 3 km upstream would be [tex]\frac{3}{x+1}[/tex].
Since both times are equal, so we can equate both expressions as:
[tex]\frac{3}{x+1}=\frac{2}{x-1}[/tex]
Cross multiply:
[tex]3(x-1)=2(x+1)[/tex]
[tex]3x-3=2x+2[/tex]
[tex]3x-2x-3=2x-2x+2[/tex]
[tex]x-3=2[/tex]
[tex]x-3+3=2+3[/tex]
[tex]x=5[/tex]
Therefore, the average speed of Kayak in still water is 5 km per hour.
