The motorboat passed 80 km against the river and returned to the point of departure

The motorboat passed 80 km against the river and returned to the point of departure, spending 1 hour less on the way back. Find the speed of the boat in a stationary bar if the current speed is 2 km / h.

1. Distance, which the motor boat passed against the stream of the river and returned back: S = 80 km;

2. Time when the boat was sailing against the stream of the river: Tpr hour;

3. Time when the boat went along the river: Tpo hour;

By the condition of the problem: To = Tpr – Tpo = 1 hour;

4. River flow speed: Vr = 2 km / h;

5. Boat speed in still water: Vl km / h;

6. Calculate To:

To = Tпр – Tпо = S / (Vл – Vр) – S / (Vл + Vр) =

S * (1 / (Vl – Vp) – 1 / (Vl + Vp) = 320 / (Vl ^ 2 – 4) = 1 hour;

Vl ^ 2 = 320 + 4 = 324;

Vl1,2 = sqrt (324) = + – 18;

A negative root is meaningless;

Vl = 18 km / h.

Answer: boat speed in still water 18 km / h.