Question

Катер отправился из пункта С по течению реки. Проехав 80 км, катер остановился. Через 3 ч после остановки катер повернул обратно и приплыл в исходный пункт С спустя 9 ч от начала движения от пункта С. Скорость течения реки равна 3 км/ч. Определите скорость катера в неподвижной воде.​

Answer 1

Ответ:

27 км/ч

Объяснение:

Искомая скорость Х в км/ч.

80:(Х+3) часов проплыл до остановки

*0/(Х-3) затратил на обратный путь.

Уравнение

80*(1/(Х+3)+1/(Х-3))=9-3

80*2Х=6*(Х*Х-9)

3Х*Х-80Х-27=0

Дискриминант:

6400+12*27=4*(1600+81)=4*41*41=82*82

Положительный корень

(80+82)/6=162/6=81/3=27 км/час

Answer 2

Problem Analysis

We are given that a boat travels from point C downstream along a river. After traveling 80 km, the boat stops. Three hours after the stop, the boat turns back and returns to point C after 9 hours from the start of the journey. We need to determine the speed of the boat in still water.

Solution

Let's assume the speed of the boat in still water is x km/h.

When the boat is traveling downstream, it benefits from the speed of the river current, which is given as 3 km/h. Therefore, the effective speed of the boat downstream is (x + 3) km/h.

When the boat turns back and travels upstream, it has to overcome the speed of the river current. Therefore, the effective speed of the boat upstream is (x - 3) km/h.

We can use the formula distance = speed × time to calculate the distances traveled by the boat downstream and upstream.

Calculation

Let's calculate the distances traveled by the boat downstream and upstream.

- Distance downstream = 80 km - Distance upstream = Distance downstream

Using the formula distance = speed × time, we can write the following equations:

- Distance downstream = (x + 3) km/h × 3 h - Distance upstream = (x - 3) km/h × 9 h

Simplifying the equations:

- 80 km = (x + 3) km/h × 3 h - 80 km = (x - 3) km/h × 9 h

Now, we can solve these equations to find the value of x, which represents the speed of the boat in still water.

Solving the Equations

Let's solve the equations to find the value of x.

From the first equation, we have:

80 km = (x + 3) km/h × 3 h

Simplifying:

80 km = 3x + 9 km/h

Subtracting 9 km/h from both sides:

80 km - 9 km/h = 3x

71 km = 3x

Dividing both sides by 3:

71 km / 3 = x

x ≈ 23.67 km/h

Therefore, the speed of the boat in still water is approximately 23.67 km/h.

Answer

The speed of the boat in still water is approximately 23.67 km/h.