Question 171131
Let {{{r}}} be the speed of the boat in still water.  If the current is 6 mph, then the speed of the boat upstream must be {{{r-6}}} and the speed of the boat downstream must be {{{r+6}}}.


Since {{{d=rt}}}, or put another way {{{r=d/t}}}, the upstream trip can be described as {{{r-6=d/5}}} and the downstream trip can be described as {{{r+6=d/3}}}


Solve both equations for d:


{{{r-6=d/5}}}
{{{5r-30=d}}}


{{{r+6=d/3}}}
{{{3r+18=d}}}


Since we have two expressions involving {{{r}}}, the speed of the boat in still water, both equal to {{{d}}}, the distance travelled, set the two expressions equal to each other.


{{{5r-30=3r+18}}}


And solve:


{{{5r-3r=18+30}}}


{{{2r=48}}}


{{{r=24}}}


Check the answer:


Still water speed:  {{{24}}}


Upstream speed: {{{24-6=18}}}


Upstream distance:  {{{d=18*5=90}}}


Downstream speed: {{{24+6=30}}}


Downstream distance:  {{{30*3=90}}}


Upstream distance equals downstream distance so the answer checks.