luvenia can row 4mph in still water. She takes as long to row 7 mi upstream as 21 mi downstream. how

The speed of the river is 2mph.

Step-by-step explanation:

I guess that we want to find the speed of the river.

First, remember the relation: speed*time = distance

If the speed of the river is Sr, when Luvenia moves downstream (in the same direction that the flow of the water) the total speed will be equal to the speed of Luvenia in still water plus the speed of the water:

Sd = 4mph + Sr

and at this speed, in a time T, she can move 21 miles, so we have:

Sd*T = (4mph + Sr) * T = 21 mi

When moving upstream, the speed will be:

Su = (4mph - Sr)

and in the same time T as before, she moves 7 miles, so we have the equation:

Su*T = (4mph - Sr) * T = 7 mi

Then we have two equations:

(4mph + Sr) * T = 21 mi

(4mph - Sr) * T = 7 mi

Now we can take the quotient of those two equations and get:

((4mph + Sr) * T) / ((4mph - Sr) * T) = 21/7

The time T vanishes, and we can solve it for Sr.

(4mph + Sr) / (4mph - Sr) = 3

4mph + Sr = 3 * (4mph - Sr) = 12mph - 3*Sr

4*Sr = 12mph - 4mph = 8mph

Sr = 8mph/4 = 2mph.