Let x be the "x-coordinate" of the intermediate "target" point D between points C and B on the opposite bank of the river.


Then the total time t(x) to get from  A to B  is


    t(x) =  +   hours.     (1)


The plot of this function is shown in the figure below, and it clearly shows that the function t(x) has a minimum between 0 and 8.




Plot y =  + 


To find the value of x which provides the minimum to t(x), take the derivative of t(x)


    t'(x) =  - ,


equate it to zero and solve the obtained equation for x


     -  = 0,

    8x = 

    64x^2 = 36(9+x^2)

    64x^2 = 36*9 + 36x^2

    64x^2 - 36x^2 = 324

    x^2 =  = 11.571

    x =  = 3.4 (approximately).



Answer.  The target point to minimize time is 3.4 kilometers from C to B,


         giving time  t(3.4) =  +  = 1.331 hours.