SOLUTION: A boat on a river travels downstream between two points, 80 mi apart, in 1 h. The return trip against the current takes 2.5 hours What is the boat's speed (in still water)?

Let  u  be the boat speed in still water (in miles per hour, mph).

Let  v  be the rate of the current, in mph.


Then  the boat's  effective speed downstream is  u+v  mph,
while the boat's  effective speed upstream   is  u-v  mph.


Now, "speed" equation for boat floating upstream is 

 = u - v    (1)    (speed upstream = the distance divided by time upstream)


Next, "speed" equation for boat floating downstream is 

 = u + v    (2)    (speed downstream = the distance divided by time  downstream)



Simplify equations (1) and (2)


u - v = 32     (3)
u + v = 80     (4)


Now add equations (3) and (4) to eliminate "v". You will get


2u = 80 + 32 = 112  ====>  v =  = 56.


ANSWER.  The rate of the boat in still water is 56 miles per hour.    ANSWER