# The motor boat passed 120 km against the river and returned to the point of departure, spending 2 hours

The motor boat passed 120 km against the river and returned to the point of departure, spending 2 hours less on the way back. Find the speed of the boat in still water if the current is 1 km / h.

x kilometers per hour – the boat’s own speed,
x – 1 kilometers per hour – boat speed against the current,
120 / (x – 1) hours – the boat spent all the way upstream.
х + 1 kilometers per hour – boat speed downstream,
120 / (x + 1) hours – the boat spent all the way downstream.
120 / (x + 1) + 2 = 120 / (x – 1).
120 * (x – 1) + 2 * (x ^ 2 – 1) = 120 * (x + 1);
x ^ 2 = 121;
Roots: -11 (speed cannot be negative) and 11.
Answer: 11 kilometers per hour is the boat’s own speed.

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