The steamer traveled 48 km along the river and the same amount upstream, spending 5 hours

The steamer traveled 48 km along the river and the same amount upstream, spending 5 hours for the entire journey. Find the speed of the steamer in still water if the river speed is 4 km / h.

1. Distance covered by the steamer along the river and back: S = 48 km;

2. River flow speed: Vр = 4 km / h;

3. Steamer speed in still water: Vп km / h;

4. Time spent on the whole journey: T = 5 hours;

T = Tpo + Tpr = S / (Vp + Vp) + S / (Vp – Vp) = S * (1 / (Vp + Vp) + 1 / (Vp – Vp) = (2 * S * Vp) / ( Vn ^ 2 – Vp ^ 2) = 5;

2 * S * Vp = 5 * (Vp ^ 2 – Vp ^ 2);

5 * Vp ^ 2 – 96 * Vp – 80 = 0;

Vp1,2 = (96 + – √ (96 ^ 2 + 4 * 5 * 80)) / 2 * 5 = (96 + – 104) / 10;

A negative root is meaningless;

Vp = (96 + 104) / 10 = 20 km / h.

Answer: the speed of the steamer in still water is 20 km / h.