The distance between the two marinas along the river is 80 km. The boat goes this way there and back in 8 hours

| August 13, 2021 | education

The distance between the two marinas along the river is 80 km. The boat goes this way there and back in 8 hours. 20 minutes. Determine the speed of the steamer in still water, considering the speed of the river flow equal to 4 km per hour.

Let the speed of the ship in still water be x.

Thus, since the current speed is 4 km / h, then the downstream speed will be: x + 4 km / h.

Upstream speed: x – 4.

8 hours 20 minutes = 8 1/3 hours.

We get the equation for the sum of time.

80 / (x + 4) + 80 / (x – 4) = 8 1/3.

80 * x – 320 + 80 * x + 320 = 8 1/3 * x ^ 2 – 133 1/3.

8 1/3 * x ^ 2 – 160 * x – 133 1/3 = 0.

x ^ 2 – 19.2 * x – 16 = 0.

D ^ 2 = (-19.2) ^ 2 – 4 * 1 * (-16) = 368.64 + 64 = 432.46.

D = 20.8.

x = (19.2 + 20.8) / 2 = 40/2 = 20 km / h.

Answer: 20 km / h.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.