The boat goes 40 km along the river to its destination and after stopping it returns to the point of departure.

The boat goes 40 km along the river to its destination and after stopping it returns to the point of departure. The speed of the boat in still water is 18 km / h, the stay lasts 1 hour, the boat returns to the point of departure 5.5 hours after leaving it. Find the speed of the river.

Let x km / h be the speed of the river.

Then (18 + x) km / h is the speed of the boat along the river.

(18 – x) km / h – speed of the boat against the stream of the river.

40 / (18 + x) h – time of boat movement along the river; 40 / (18 – x) h – the time of movement of the boat against the stream of the river.

Discarding the boat stay time from 5.5 hours, we will compose the equation:

40 / (18 + x) + 40 / (18 – x) = 4.5;

40 (18 – x) + 40 (18 + x) = 4.5 (18 + x) (18 – x);

720 – 40x + 720 + 40x = 4.5 (324 – x);

1440 = 1458 – 4.5x ^ 2;

4.5x ^ 2 = 1458 – 1440;

4.5x ^ 2 = 18;

x ^ 2 = 18 / 4.5;

x ^ 2 = 4;

x = 2 (km / h) – river flow speed.

Answer: 2 km / h.