Against the current the effective speed (the speed relative to the river bank) is


u - v =  = 35  miles per hour.     (1)   (u = the speed of the motorboat in still water;  v = the speed of the current)



With the current, the effective speed is

u + v =  =  45 miles per hour.     (2)



Add equations (1) and (2)


2u = 35 + 45 = 80  ====>  u = 80/2 = 40 mph is the speed of the motorboat in still water.    ANSWER



Subtract eq(1) from eq(2)

2v = 45 - 35 = 10  ====>  v = 10/2 = 5 mph  is the speed of the current.     ANSWER

    1.  The effective speed of a boat traveling with    a current is the sum        of the two speeds.

    2.  The effective speed of a boat traveling against a current is the difference of the two speeds.

    3.  It gives a system of two equations in two unknowns, which fits very well to be solved by the elimination method.