The boat covered 80 km along the river and 90 km along the lake, spending 9 hours for the entire journey.

The boat covered 80 km along the river and 90 km along the lake, spending 9 hours for the entire journey. find the speed of the boat if the river speed is 2 km / h.

Let the speed of the boat along the lake (or the own speed of the boat) be x km / h, then the speed of the boat along the river is (x + 2) km / h. The boat covered 80 kilometers along the river in 80 / (x + 2) hours, and 90 kilometers along the lake in 90 / x hours. According to the condition of the problem, it is known that the boat spent (80 / (x + 2) + 90 / x) hours or 9 hours for the entire journey. Let’s make an equation and solve it.

80 / (x + 2) + 90 / x = 9;

O.D.Z. x ≠ 0, x ≠ -2;

80x + 90 (x + 2) = 9x (x + 2);

80x + 90x + 180 = 9x ^ 2 + 18x;

9x ^ 2 + 18x – 80x – 90x – 180 = 0;

9x ^ 2 – 152x – 180 = 0;

D = b ^ 2 – 4ac;

D = (-152) ^ 2 – 4 * 9 * (-180) = 23104 + 6480 = 29584; √D = 172;

x = (-b ± √D) / (2a);

x1 = (152 + 172) / (2 * 9) = 324/18 = 18 (km / h) – boat speed;

x2 = (152 – 172) / 18 = -20/18 – the speed cannot be negative.

Answer. 18 km / h