Question 419040
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The current of a river is 2 miles per hour. A boat travels to a point 8 miles upstream and back again in 3 hours. 
What is the speed of the boat in still water?
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        The solution and the answer in the post by @mananth both are incorrect.

        I came to bring a correct solution.



<pre>
speed in still water =  x mph.			

current speed 		2 mph.		

					
upstream speed   = x-2 mph.		
downstream speed = x+2 mph.			
					
Distance = 	8 miles.			
					

Time equation

    {{{8/(x+2)}}} + {{{8/(x-2)}}} = 3				.


    LCD = (x-2)*(x+2)								

    8*(x-2) + 8*(x+2) = 3				

    8x - 16+ 8x + 16 = 3(x^2-4)

    16x = 3x^2 - 12						

    3x^2 - 16x - 12=0	


Use the quadratic formula 

    b^2 - 4ac = (-16)^2 - 4*3*(-12) = 256 + 144 = 400

    x = {{{(16 +- sqrt(400))/6}}}				


Use positive root {{{(16 + 20)/6}}} = {{{36/6}}} = 6.


<U>ANSWER</U>.  The speed of the boat in still water is 6 mph.
</pre>

Solved correctly.