The motor boat passed 192 km against the stream of the river and returned to the point of departure, spending 4 hours

The motor boat passed 192 km against the stream of the river and returned to the point of departure, spending 4 hours less on the way back than the way against the stream, find the speed of the boat in still water if the river speed is 4 km

Suppose that the speed of a motor boat in still water is x km / h, then it will go along the river at a speed of x + 4 km / h, and against the current at a speed of x – 4 km / h.
According to the condition of the problem, we compose and solve the equation:
192 / (x – 4) – 192 / (x + 4) = 4,
192 * x + 768 – 192 * x + 768 = 4 * (x² – 16),
4 * x² – 1600 = 0,
4 * х² = 1600,
х² = 1600: 4,
x² = 400,
x = 20 (km / h) – speed of a motor boat in still water.
Answer: 20 km / h.



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