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.