SOLUTION: A motorboat takes 3 hours to travel 108km going upstream. The return trip takes 2 hours going downstream. What is the rate of the boat in still water and what is the rate of the cu

Let u be the motorboat speed in still water and v be the current rate.


The effective speed going upstream is 

 =  = 36 km/h.


It is the DIFFERENCE of the motorboat speed in still water and the rate of the current. It gives you your first equation

u - v = 36.    (1)



The effective speed going downstream is 

 =  = 54 km/h.


It is the SUM of the motorboat speed in still water and the rate of the current. It gives you your second equation

u + v = 54.    (2)


Thus you have this system of two equations in 2 unknowns

u - v = 36,    (1)   and
u + v = 54.    (2)


Add the two equations. You will get

2u = 36 + 54 = 90  ====>  u =  = 45 km/h.


So, you just found the speed of the motorboat in still water.  It is  45 km/h.

Then from the equation (2) you get  v = 54 = 45 = 9 km/h is the current rate.


Answer.  The speed of the motorboat in still water is  45 km/h.

         The current rate is 9 km/h.