SOLUTION: a boat traveled 336 miles downstream and back. The trip downstream took 12 hours. The trip back took 14 hours. what is the speed of the boat in still water? What is the speed of th

                  SPEED      TIME     DISTANCE

DOWN              r+c        12       168

UP                r-c        14       168

Total                                336

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


The effective speed going downstream is 

 =  = 28 miles per hour.


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

u + v = 28.    (1)



The effective speed going upstream is 

 =  = 24 miles per hour.


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

u - v = 24.    (2)


Thus you have this system of two equations in 2 unknowns

u + v = 28,    (1)   and
u - v = 24.    (2)


Add the two equations. You will get

2u = 28 + 24 = 52  ====>  u =  = 26 mph.


So, you just found the speed of the motorboat in still water.  It is  26 mph.

Then from the equation (1) you get  v = 28 - 26 = 2 mph is the current rate.


Answer.  The speed of the motorboat in still water is  26 mph.

         The current rate is 2 km/h.