The boat set off at 10 o’clock in the morning, walked 8 km against the stream of the river and made a stop for 1 hour.

The boat set off at 10 o’clock in the morning, walked 8 km against the stream of the river and made a stop for 1 hour. After that, he walked another 30 km downstream and arrived at his destination at 13 o’clock. Find your own speed of the boat if the river speed is 2 km / h.

1. We take as x (km / h) the speed of a river vessel in still water (own speed).

2. Its speed when moving down the river (x + 2) km / h, the speed of a river vessel when moving up the river (x – 2) km / h.

3. The time spent by the river vessel on the way:

13 hours – 10 hours – 1 hour (stop duration) = 2 hours.

4. Let’s make the equation:

8 / (x – 2) + 30 / (x +2) = 2;

38x – 44 = 2x² – 8;

x² – 19x + 18 = 0;

The first value x = (19 + √361 – 4 x 18) / 2 = (19 + √289) / 2 = (19 + 17) / 2 = 18.

The second value is x = (19 – 17) / 2 = 1. Not accepted.

Answer: the speed of a river vessel in still water (own speed) is 18 km / h.