# The distance between points A and B is 36 km. The boat first sailed along the river from point A

The distance between points A and B is 36 km. The boat first sailed along the river from point A to point B, and then back. The boat spent 5 hours for the entire journey. The speed of the river is 3 km / h. Find the speed of the boat in still water.

1. The distance between points A and B is equal to: S = 36 km;

2. Time for sailing the boat there and back: T = 5 hours;

3. Own speed of the boat: Vc km / h;

4. River flow speed: Vp = 3 km / h;

5. The equation of motion of the boat:

T = Tno + Tnp = S / Vno + S / Vnp =

S / (Vc + Vp) + S / (Vc – Vp) = 36 / (Vc + 3) + 36 / (Vc – 3) = 5;

36 * (Vc – 3 + Vc + 3) / (Vc² – 9) = 5;

72 * Vc = 5 * (Vc² – 9) = 5 * Vc² – 45;

5 * Vc² – 72 * Vc – 45 = 0;

Vc1,2 = (72 + – sqrt (72² + 4 * 5 * 45) / (2 * 5) = (72 + – 78) / 10;

A negative root is meaningless;

Vc = (72 + 78) / 10 = 15 km / h.

Answer: the boat’s own speed is 15 km / h.

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