SOLUTION: A boat on a river travels downstream between two points, 20 miles apart, in one hour. The return trip against the current takes 2 1/2 hours. What is the speed, and how fast does th

Let u = speed of the boat in still water (miles per hours), and

    v = speed of the current.


Then you have these two equation 


    u + v =       (1)   effective rate of the boat traveling downstream

    u - v =    (2)  effective rate of the boat traveling upstream  (notice   =  hours)


Equivalently


    u + v = 20    (3)

    u - v = 8     (4)


Add the equations (3) and (4) to get


    2u = 20 + 8 = 28,  ====>  u = 28/2 = 14 mph  is the boat speed in still water


Then from equation (3)    v = 20 - 14 = 6 mph is the speed of the current.