The boat traveled 3 km downstream of the river 30 minutes faster than 8 km upstream. The boat’s own speed is 15 km

The boat traveled 3 km downstream of the river 30 minutes faster than 8 km upstream. The boat’s own speed is 15 km / h. Let X km / h be the speed of the river. Make an equation.

Let x km / h be the speed of the river, then the speed of the boat along the river is (15 + x) km / h, and the speed of the boat against the river is (15 – x) km / h. The boat covered 3 kilometers along the river in 3 / (15 + x) hours, and 8 kilometers against the river in 8 / (15 – x) hours. According to the condition of the problem, it is known that the boat spent less time on the path along the river than on the path against the course of the river by (8 / (15 – x) – 3 / (15 – x)) hours or 30 minutes = 1/2 hour … Let’s make an equation and solve it.

8 / (15 – x) – 3 / (15 + x) = 1/2;

O.D.Z. x ≠ 15;

8 * 2 (15 + x) – 3 * 2 (15 – x) = 15² – x²;

240 + 16x – 90 + 6x = 225 – x²;

x² + 22x – 75 = 0;

D = b² – 4ac;

D = 22² – 4 * 1 * (-75) = 784;

x = (-b ± √D) / (2a);

x = (-22 ± √784) / (2 * 1) = (-22 ± 28) / 2;

x1 = (-22 + 28) / 2 = 3 (km / h);

x2 = (-22 – 28) / 2 <0 – the speed cannot be negative.

Answer. The speed of the river is 3 km / h.