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. What is the average speed of the kayak in still water?

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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 .

Speed of kayak downstream would be speed of kayak in still water plus speed of the current that is .

Time taken to travel 2 km upstream would be .

Time taken to travel 3 km upstream would be .

Since both times are equal, so we can equate both expressions as:

Cross multiply:

Therefore, the average speed of Kayak in still water is 5 km per hour.

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see explanation

step-by-step explanation:

a

(6r + 7) + (13 + 7r) ( remove brackets and collect like terms )

= 6r + 7 + 13 + 7r

= 13r + 20

b

remove brackets and collect like terms

13 - r - 1 + r

= 12 - r

c

remove brackets and collect like terms

= - 8 - r + 2r - 4

= - 12 + r

d

remove brackets and collect like terms

= 7r - - - 6r

[-   - = - - = - ]

= r -