The motor boat covered 10 km along the river 12 km against the current, spending 2 hours

The motor boat covered 10 km along the river 12 km against the current, spending 2 hours for the entire journey. The river’s speed is 3 km / h. Find the speed of the boat.

1) Suppose x km / h is the boat’s own speed.

2) Then (x + 3) km / h is its speed of movement along the river, (x – 3) km / h – against the stream.

3) 10 / (x + 3) hours – the time of boat movement along the river, 12 / (x – 3) hours – against the current.

4) In total, the boat was on the way for 2 hours, so we write down:

10 / (x + 3) + 12 / (x – 3) = 2.

5) Solve the equation:

10 * (x – 3) + 12 * (x + 3) = 2 * (x ^ 2 – 9);

10x – 30 + 12x + 36 = 2x ^ 2 – 18;

22x + 6 = 2x ^ 2 – 18;

2x ^ 2 – 22x – 24 = 0;

x ^ 2 – 11x – 12 = 0;

x1 = 12, x2 = -1 – the roots of the quadratic equation.

6) x2 = -1 is not a solution to the problem.

7) It turns out that x = 12 km / h is the boat’s own speed.

Answer: 12 km / h.