The boat traveled 15 km along the river and 4 km along the lake, spending 1 hour for the whole journey

The boat traveled 15 km along the river and 4 km along the lake, spending 1 hour for the whole journey. Find your own speed of the boat if the river speed is 4 km / h.

Let’s take the boat’s own speed as x, then:

x + 4 – speed of the boat along the river;

4: x = 4 / x – time of movement along the lake;

15 / (x + 4) – river time.

Since all the time was 1 hour, we get the equation:

4 / x + 15 / (x + 4) = 1;

4x + 16 + 15x = x ^ 2 + 4x;

x ^ 2 – 15x – 16 = 0;

x12 = (15 + -√ (225 – 4 * (-16)) / 2 = (15 + – 17) / 2.

x1 = (15 + 17) / 2 = 16; x2 = (15 – 17) / 2 = -1 – the root has no physical meaning.

Answer: the boat’s own speed is 16 km / h.