The boat covered 40 km along the river and 6 km against the current

The boat covered 40 km along the river and 6 km against the current, spending 3 hours for the entire journey, which is equal to the boat’s own speed if the current speed is 2 km / h.

1. Distance covered by the boat along the river: S1 = 40 km;

2. Distance covered by the boat against the current: S2 = 6 km;

3. Time spent by the boat for the whole journey: T = 3 hours;

4. Time of sailing along the river: T1 km;

5. Swimming time upstream of the river: T2 km;

6. Calculate:

Т = Т1 + Т2 = S1 / (Vк + Vр) + S / (Vк – Vр) =

40 / (Vk + 2) + 6 / (Vk – 2) = 3 hours;

(46 * Vk – 68) / (Vk ^ 2 – 2 ^ 2) = 3;

3 * Vk ^ 2 – 46 * Vk + 56 = 0;

Vк1,2 = (46 + – sqrt (46 ^ 2 – 4 * 3 * 56)) / (3 * 2) =

(46 + – sqrt (1444)) / 6 = (46 + – 38) / 6;

Vк1 = (46 – 38) / 6 = 8/6 km / h (less than the speed of the river, does not satisfy);

Vк = (46 + 38) / 6 = 14 km / h.

Answer: the boat’s own speed is 14 km / h.