Question 144580
Let {{{s}}}= speed of the boat in still water
The current = {{{3}}} mi/hr
In words:
(distance traveled upriver)/(rate going upriver)
+ (distance traveled downriver)/(rate going downriver) = 9 hrs
{{{60 / (s - 3) + 60 / (s + 3) = 9}}}
multiply both sides by {{{(s - 3)(s + 3)}}}
{{{60*(s + 3) + 60*(s - 3) = 9(s^2 - 9)}}}
divide both sides by {{{3}}}
{{{20*(s + 3 + s - 3) = 3s^2 - 27}}}
{{{40s = 3s^2 - 27}}}
{{{3s^2 - 40s - 27 = 0}}}
solve using quadratic fornula
{{{s = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{s = (-(-40) +- sqrt( (-40)^2-4*3*(-27) ))/(2*3) }}}
{{{s = (40 +- sqrt(1600 + 324 )) / 6 }}}
{{{s = (40 +- sqrt(1924 )) / 6 }}}
{{{s = (40 + 43.863)/6}}}
{{{s = 83.86/6}}}
{{{s = 13.98}}}mi/hr
If you plug this back into the original equation, it checks out