The boat traveled 12 km along the river and 4 km against the current, spending 2 hours on the whole path.

The boat traveled 12 km along the river and 4 km against the current, spending 2 hours on the whole path. What is the boat’s own speed if the current speed is 4 km / h.

Let’s designate: x km / h – own speed of the boat.
According to the condition of the problem, an equation was drawn up:
12 / (x + 4) + 4 / (x – 4) = 2;
(12 * (x – 4) + 4 * (x + 4)) / (x ^ 2 – 16) = 2;
12x – 48 + 4x + 16 = 2 * (x ^ 2 – 16);
16x – 32 = 2×2 – 32;
2x ^ 2 – 16x – 32 + 32 = 0;
2x ^ 2 – 16x = 0;
x ^ 2 – 8x = 0;
x * (x – 8) = 0;
x = 0 or x – 8 = 0;
x = 0 or x = 8;
Since the boat’s own speed cannot be equal to 0, it is equal to 8 km / h.
Answer: the boat’s own speed is 8 km / h.