The boat passed 7 km along the river and 10 km upstream, spending 30 minutes on the first route. less than the second.

The boat passed 7 km along the river and 10 km upstream, spending 30 minutes on the first route. less than the second. Find the speed of the boat against the current of the river if the speed of the current is 12 km / h

1. Distance traveled by the boat along the river: Sno = 7 km;
2. Distance, which the boat passed against the current: Snp = 10 km;
3. The swimming time upstream is longer by: To = 0.5 hours;
4. The boat’s own speed is equal to: Vc km / h;
5. River flow speed: Vp = 12 km / h;
6. We compose the equation of motion of the boat:
Tnp – Tno = To;
Snp / (Vc – Vp) – Sno / (Vc + Vp) = To;
10 / (Vc – 12) – 7 / (Vc + 12) = 0.5;
10 * Vc + 120 – 7 * Vc + 84 = 0.5 * (Vc² – 12²);
0.5 * Vc² – 3 * Vc – 276 = 0;
Vc² – 6 * Vc – 552 = 0;
Vc1,2 = 3 + – sqtrt (3² + 552) = 3 + – 23.7;
A negative root is meaningless;
Vc = 3 + 23.7 = 26.7 km / h (the check is being carried out);
Vnp = Vc – Vp = 26.7 – 12 = 14.7 km / h.
Answer: the speed of the boat against the flow of the river is 14.7 km / h.