Question 1190128
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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)?
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<pre>
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 

{{{80/2.5}}} = u - v    (1)    (speed upstream = the distance divided by time upstream)


Next, "speed" equation for boat floating downstream is 

{{{80/1}}} = 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 = {{{112/2}}} = 56.


<U>ANSWER</U>.  The rate of the boat in still water is 56 miles per hour.    <U>ANSWER</U>
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Solved.