On a certain river, a paddleboat travels 12 miles upstream (against the current) in the same amount of time it travels 20 miles downstream (with the current). if the current of the river is 2 miles per hour, determine the speed of the boat in still water.

We will take velocity of the boat Vb and velocity of the river Vr=2 mph

Distance D1=12 miles and distance D2=20 miles and t is the time.

First equation is (Vb-Vr) * t = D1 and the second is (Vb+Vr) * t = D2

When we replace data we have we get

(Vb-2) *t = 12  and (Vb+2) * t = 20

From the first equation t= 12/(Vb-2)

From the second equation t=20/(Vb+2)

If the left sides of equations are equal then the right sides are equal too,

and we get   12/(Vb-2)=20/(Vb+2) then we multiply crosswise and get

12*(Vb+2)=20*(Vb-2) => 12Vb+24=20Vb-40 => 20Vb-12Vb=40+24 =>

8Vb=64 => Vb=64/8=8mph  Velocity ( or speed) of the boat is Vb= 8mph

Good luck!!!

step-by-step explanation: