The speed of the boat in still water is 20 km / h. The route is 396 km long downstream of the river

The speed of the boat in still water is 20 km / h. The route is 396 km long downstream of the river, it swims 4 hours faster than against the current. Find the speed of the river.

Let the speed of the river flow “X”. Then the speed of the boat downstream will be “20 + X”, and against the current “20 – X”. Using the formula t = S / V, compose and solve the equation:

396 / (20 + X) + 4 = 396 / (20 – X);

(7920 – 396X + 1600 – 4X ^ 2 – 7920 – 396X) / (20 + X) * (20 – X) = 0;

X ≠ -20; X ≠ 20;

–4X ^ 2 – 792X + 1600 = 0;

X ^ 2 + 198X – 400 = 0;

D = 39204 + 1600 = 40804;

X1 = (-198 – 202) / 2 = -200 – does not meet the conditions of the problem;

X2 = (-198 + 202) / 2 = 2 (km / h).

Answer: the speed of the river is 2 km / h.