# The boat sailed 40 km behind the stream of the river and 16 km against the stream, using 3 hours

The boat sailed 40 km behind the stream of the river and 16 km against the stream, using 3 hours for the entire journey. What is the proper speed of the boat if the current speed is 2 km / h?

1. Let X km / h be the speed of the boat in water without current.

The speed of the river is 2 km / h.

Then the boat floats with the current (X + 2) km / h, against (X – 2) km / h.

2. According to the condition of the problem, the boat first covered 40 km downstream.

His travel time on this section is 40 / (X + 2) hours.

Then he moved 16 km against the current.

At the same time, I spent 16 / (X – 2) hours.

3. The whole journey took 3 hours.

40 / (X + 2) + 16 / (X – 2) = 3.

40 * X – 80 + 16 * X + 32 = 3 * X * X – 3 * 4.

3 * X * X – 56 * X + 36 = 0.

Discriminant D = 56 * 56 – 4 * 3 * 36 = 52 * 52.

X1 = (56 + 52) / 6 = 108/6 = 18 km / h.

X2 = (56 – 52) / 6 = 4/6 km / h – not suitable, since it is less than the speed of the river.

Answer: The speed of the boat is 18 km / h.

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