Question 800877
x = rate in still water
y = rate of the current water
(Really, speeds, not rates, but certainly yes, ratios)


WHICHWAY_____________speed_______________time____________distance
DOWN_________________x+y_________________2_______________(___)
UP___________________x-y_________________5_______________(___)


Be aware, we use r*t=d, for uniform rates for movement or travel or transport, r for rate, t for time, d for distance.
Also that the speeds are in order, {{{x-y<x+y}}}.


Completing the data table,


WHICHWAY_____________speed_______________time____________distance
DOWN_________________x+y_________________2_______________(x+y)2
UP___________________x-y_________________5_______________(x-y)5
Total_____________________________________________________20


That is the extent of the data analysis.  This information gives you a distance sum of {{{(x+y)*2+(x-y)*5=20}}}, 
{{{2x+2y+5x-5y=20}}}
{{{highlight(7x-3y=20)}}}
Which is a an infinite set of solutions for x and y, but with some restrictions.
You can easily enough find those restrictions symbolically, and you could also make the linear graph and see the restrictions on x and y graphically.


Any solution, (x,y) must be in the Quadrant 1:

{{{graph(300,300,-2,10,-2,10,(7x-20)/3)}}}


{{{x>2&6/7}}} miles per hour and {{{y>0}}} miles per hour;
You would pick one variable and assign a value and compute the corresponding value of the other variable.