The distance between quays A and B is 18 km. A raft set off from A to B along the river, and after 30 minutes

The distance between quays A and B is 18 km. A raft set off from A to B along the river, and after 30 minutes a motor boat set off for it, which, having arrived at point B, immediately turned back and returned to A. By this time, the raft had covered 9 km. Find the speed of the boat in still water if the river speed is 50 m / min.

30: 5 = 6 (h) – the time spent by the raft, as it floats along the river;
6-1 = 5 (h) – the boat spent all the way.
Let C = the boat’s own speed – x km / h, then the downstream speed is (x + 5) km / h. It is known that the distance is 60 km, then the time is 60 / (x + 5). Against the current, the speed is (x-5) km / h, then the time is 60 / (x-5) h. Let’s compose and solve the equation:
60 / (x + 5) + 60 / (x-5) = 5;
(60 (x-5) +60 (x + 5)) / (x ^ 2-25) = 5 * (x ^ 2-25);
60x-300 + 60x + 300 = 5 (x ^ 2-25);
120x = 5x ^ 2-125;
120x-5x ^ 2 + 125 = 0;
x ^ 2-24x- 25 = 0;
D = (-24) ^ 2 – 4 * (- 25) = 576 + 100 = 676;
x₁ = (24- root 676) / 2 = (24-26) / 2 = -2 / 2 = -1 – does not satisfy the condition of the problem;
x₂ = (24 + 26) / 2 = 50/2 = 25 – the boat’s own speed;
Answer: 25 km / h boat speed in still water.