Question 153431
Let x be the speed of the boat in still water.
So
The boat's downstream speed relative to the riverbank is x+3.
The boat's upstream speed relative to the riverbank is x-3. 
Time spend traveling downstream is {{{14/(x+3)}}}
Time spend traveling upstream is {{{8/(x-3)}}}
As the time spend traveling downstream is the same as the time spend traveling upstream, we have:
{{{14/(x+3)=8/(x-3)}}}
Solving for x, we have:
{{{(x+3)(x-3)*(14/(x+3))=(x+3)(x-3)*(8/(x-3))}}} (multiply both side by (x+3)(x-3)
{{{14(x-3)=8(x+3)}}}
{{{14x-42=8x+24}}}
{{{6x=66}}}
{{{x=66/6}}}
{{{x=11}}}
So the speed of the boat in still water is 11 miles per hour.