SPEED       TIME           DISTANCE

A to B       4-k          1                 d

B to C       4+k                      

Let "c" be the rate of current, in miles.

Then  the rate moving  upstream    is (4-c) miles per hour, 

while the rate moving  downstream  is (4+c) miles per hour.



Let d(A,B) be the distance from A to B, and let d(B,C) is the distance from B to C.



Since the travel upstream from A to B took 1 hour, the distance 

    d(A,B) = the rate moving  upstream * 1 hour = (4-c)*1 = 4-c miles.



Since the travel downstream from B to C took 12 minutes =  of an hour, the distance 

    d(B,C)) = the rate moving  downstream *  hour =  miles.



From the condition, you are given that  d(B,C) = .d(A,C).


It gives you an equation


    .(4 + c) = .(4 - c).


It is your basic equation.  The setup is just completed.



To solve the equation, multiply both sides by 15.  You will get

    3*(4 + c) = 5*(4 - c)

    12 + 3c = 20 - 5c

    3c + 5c = 20 - 12

    8c      = 8

     c = 1  mile per hour.



ANSWER.  The rate of the current is  1 mile per hour.