Question 170853
Let s=speed of stream


Remember, the distance-rate-time formula is 


{{{d=rt}}}



{{{d/r=t}}} Divide both sides by r to solve for t.



{{{t=d/r}}} Rearrange the equation.



So when she goes upstream (against the current), the stream is slowing her down. So this means that {{{r=9-s}}} and {{{d=12}}}. So the equation for the upstream portion of the journey is:


{{{t=12/(9-s)}}} 


When she goes downstream (with the current), the stream is speeding her up. So this means that {{{r=9+s}}} and {{{d=12}}}. So the equation for the downstream portion of the journey is:


{{{t=12/(9+s)}}}



Now simply add these two equations together to get the total time 3 hours like this:



{{{12/(9-s)+12/(9+s)=3}}}



{{{12(9+s)+12(9-s)=3(9-s)(9+s)}}} Multiply both sides by the LCD {{{(9-s)(9+s)}}} to clear the fractions.



{{{12(9+s)+12(9-s)=3(81-s^2)}}} FOIL



{{{108+12s+108-12s=243-3s^2}}} Distribute



{{{216=243-3s^2}}} Combine like terms.



{{{-27=-3s^2}}} Subtract 243 from both sides.



{{{9=s^2}}} Divide both sides by {{{-3}}}.



{{{s=3}}} Take the square root of both sides. Note: only the positive square root is considered. 


So the speed of the stream is 3 km/hr