# The motor boat drove 10 km / h along the river and 12 km / h against the current, spending 2 hours

The motor boat drove 10 km / h along the river and 12 km / h against the current, spending 2 hours and 20 minutes for the entire journey. Find the speed of the river if the boat’s own speed is 10 km / h.

We denote the speed of the river flow by x km / h, then the speed along the river is (10 + x) km / h, the speed against the stream is (10 – x) km / h.
Let’s write down the time spent on the movement with the current and against:
10 / (10 + x) (h) – time downstream;
12 / (10 – x) (h) – time upstream.
In total, the whole journey took 2 hours 20 minutes = 2 1/3 hours, we draw up the equation.
10 / (10 + x) + 12 / (10 – x) = 2 1/3
300 – 30x + 360 + 36x = 700 – 7x²
7x² + 6x – 40 = 0
D = b² – 4 * a * c = 36 – 4 * 7 * (-40) = 1156, D> 0, two roots.
x1 = (-6 + 34) / 14 = 2;
x2 = (-6 – 34) / 14 = -40 / 14 = – 2.85714 (negative root is not suitable).
Answer: the speed of the river is 2 km / h.

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