The motor boat passed 255 km against the river and returned to the point of departure

The motor boat passed 255 km against the river and returned to the point of departure, spending 2 hours less on the way back. Find the speed of the boat in still water if the current is 1 km / h.

1) Let x km / h be the speed of a motor boat in still water, i.e. her own speed.

2) (x + 1) km / h – boat speed along the river, (x – 1) km / h – upstream.

3) 255 / (x – 1) hours – the time of boat movement against the river, 255 / (x + 1) hours – downstream.

4) From the condition of the problem, you can write:

255 / (x – 1) – 255 / (x + 1) = 2.

5) Let’s solve the equation:

255 * (x + 1) – 255 * (x – 1) = 2 * (x ^ 2 – 1);

255x + 255 – 255x + 255 = 2x ^ 2 – 2;

510 + 2 = 2x ^ 2;

512 = 2x ^ 2;

x ^ 2 = 512: 2;

x ^ 2 = 256;

x = √256;

x1 = 16, x2 = -16.

6) x = -16 is not a solution to the problem.

7) We get that x = 16 km / h – the speed of the boat in still water.

Answer: 16 km / h.