The motor boat passed from one pier to another, the distance between which along the river is 16 kilometers

| January 3, 2021 | education

The motor boat passed from one pier to another, the distance between which along the river is 16 kilometers, made a stop for 40 minutes and returned back after 3 2 / 3h (shot) after the start of the trip Find the speed of the river if it is known that the speed of the motor boat in still water is 12 kilometers per hour.

1. Distance between quays: S = 16 km;
2. Speed of a motor boat in still water: Vl = 12 km / h;
3. Boat sailing time: T = 3 hours 40 minutes;
4. Standing time: To = 40 min;
5. Time of the boat’s clean running without stopping: Td hour;
Td = T – To = 3 * (2/3) – 2/3 = 3 hours;
6. Time of boat sailing with the current and against:
Td = Tpo + Tpr = S / (Vl + Vp) + S / (Vl – Vp) = 16 / (12 + Vp) + 16 / (12 – Vp) = 3;
192 – 16 * Vp + 16 * Vp + 192 = 432 – 3 * Vp ^ 2;
3 * Vp ^ 2 = 48;
Vp ^ 2 = 16;
Vр1,2 = + – 4 km / h;
A negative root is meaningless;
Vр = 4 km / h.
Answer: the speed of the river is 4 km / h.



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