The tourist rode a motor boat up the river for 25 km, and went back down on a raft

The tourist rode a motor boat up the river for 25 km, and went back down on a raft. In a boat, he sailed 10 hours less than on a raft. Find the current speed if the boat speed in still water is 12 km / h.

Let the speed of the river flow be x km / h, then the speed of the boat against the river flow is (12 – x) km / h, and the speed of the raft is equal to the speed of the river flow x km / h. The boat passed the distance of 25 kilometers against the river in 25 / (12 – x) hours, and the raft the same distance in 25 / x hours. By the condition of the problem, it is known that the boat spent less time on its way than the raft by (25 / x – 25 / (12 – x)) hours or 10 hours. Let’s make an equation and solve it.

25 / x – 25 / (12 – x) = 10;

(25 (12 – x) – 25x) / (x (12 – x)) = 10;

O.D.Z. x ≠ 0; x ≠ 12;

25 (12 – x) – 25x = 10x (12 – x);

300 – 25x – 25x = 120x – 10x ^ 2;

10x ^ 2 – 120x – 50x + 300 = 0;

10x ^ 2 – 170x + 300 = 0;

x ^ 2 – 17x + 30 = 0;

D = (-17) ^ 2 – 4 * 1 * 30 = 289 – 120 = 169; √D = 13;

x = (-b ± √D) / (2a);

x1 = (17 + 13) / 2 = 30/2 = 15 (km / h) – the current speed cannot be (in this case) more than 12 km / h, because the boat will not be able to sail against the current of the river;

x2 = (17 – 13) / 2 = 4/2 = 2 (km / h).

Answer. 2 km / h.