The boat covered 25 km along the river and 3 km against the current, spending 2 hours for the whole journey.

The boat covered 25 km along the river and 3 km against the current, spending 2 hours for the whole journey. Find your own speed of the boat if the river speed is 3 km / h.

Let the boat’s own speed be x km / h, then the speed of the boat along the river is (x + 3) km / h, and the speed of the boat against the river is (x – 3) km / h. The boat covered 25 kilometers along the river in 25 / (x + 3) hours, and 3 kilometers against the river in 3 / (x – 3) hours. By the condition of the problem, it is known that the boat spent (25 / (x + 3) + 3 / (x – 3)) hours or 2 hours for the entire journey. Let’s make an equation and solve it.
25 / (x + 3) + 3 / (x – 3) = 2;
O.D.Z. x ≠ ± 3;
25 (x – 3) + 3 (x + 3) = 2 (x² – 9);
25x – 74 + 3x + 9 = 2x² – 18;
28x – 66 = 2x² – 18;
2x² – 28x – 18 + 66 = 0;
2x² – 28x + 48 = 0;
x² – 14x + 24 = 0;
D = b² – 4ac;
D = (-14) ² – 4 * 1 * 24 = 196 – 96 = 100; √D = 10;
x = (-b ± √D) / (2a);
x1 = (14 + 10) / 2 = 12 (km / h);
x2 = (14 – 10) / 2 = 4/2 = 2 (km / h) – the speed of the boat cannot be less than the speed of the river, because the boat will not be able to sail against the current.
Answer. 12 km / h.