c   speed of stream current --- UNKNOWN in this example
r   speed of paddle boat if no current--- 8
t   time either direction -- UNKNOWN in this example
d   downstream distance ---  4
u   upstream distance  --- 2

                  SPEED        TIME       DISTANCE
DOWNSTREAM        r+c           t           d
UPSTREAM          r-c           t           u

Let "v" be the speed of the river (or, better to say, current rate), in km/h.

Then the speed of the boat downstream is (8+v) km/h (relative to the river banks),

and  the speed of the boat downstream is (8-v) km/h.


Therefore, the time for traveling 4 km downstream is  hours,

and        the time for traveling 2 km   upstream is  hours.


According to the condition, time  is the same as time , which gives you an equation

 = .    (1)


It is your equation to find the unknown "v". To solve it, multiply both sides of (1) by (8+v)*(8-v). You will get

4*(8-v) = 2*(8+v).


Simplify and solve for v:

32 - 4v = 16 + 2v  --->  32 - 16 = 2v + 4v  --->  6v = 16  --->  v =  =  km/h.

Answer.  The current rate is  km/h =  km/h.

Check.  Speed downstream is  =  =  km/h;  Time downstream is  =  =  =  of an hour.

        Speed   upstream is  =  =  km/h;  Time   upstream is  =  =  =  of an hour.