From the condition, you have these two equations


    18/3 = 6 = k + c   (1)    (the effective speed downstream)

    18/9 = 2 = k - c   (2)    (the effective speed upstream)


Again, you have these two equations


    k + c = 6          (1)

    k - c = 2          (2)


Add these two equations. You will get

    2k    = 6 + 2 = 8;  hence  k = 8/2 = 4  is the speed of the kayak in still water.


Next, substitute  k= 4 into equation (1).  You will get

    4 + c = 6,  which  implies  c = 6-4 = 2.


ANSWER.  The kayak speed in still water is 4 miles per hour.

         The speed of the current is  2 miles per hour.