Question 786281
r = speed of boat without any river current


DIRECTION_________rate_____________time__________distance
down_____________r+7_______________(___)_________72
up_______________r-7_______________(___)_________72
Total________________________________3


Key concept among the numbers {{{r*t=d}}} where r is rate, t is time, d is distance.  Using this formula allows us {{{t=d/r}}}



DIRECTION_________rate_______________time__________distance
down_____________{{{r+7}}}_______________{{{72/(r+7)}}}_________72
up_______________{{{r-7}}}_______________{{{72/(r-7)}}}_________72
Total_________________________________3



The time sum should be obvious.  {{{highlight(72/(r+7)+72/(r-7)=3)}}}
Multiply left and right by {{{(r+7)(r-7)}}}, and THEN continue to simplify, finally solving for r.  




Alternatively, {{{72(1/(r+7)+1/(r-7))=3}}}
{{{72((r-7+r+7)/(r^2-49))=3}}}-------(maybe you could keep intermediate steps {{{in your head as did I)}}}
{{{72(2r)=3(r^2-49)}}}
{{{24*2r=r^2-49}}}
{{{r^2-48r-49=0}}}
-Use general solution to quadratic formula-
{{{r=(48+sqrt(48^2-4(-49)))/2=(48+sqrt(48^2+196))/2=(48+50)/2}}}
{{{r=98/2=49}}}
Boat speed in still water, 49 mph.