Question

Из пункта А в пункт В, расстояние между которыми 120 км,по течению реки отплыла лодка и через 12 часов прибыла в пункт В. на обратный путь лодка потратила 20 часов.найти собственную скорость лодки.

Answer 1

Найдем скорость по течению:
120/12=10 км/час
Найдем скорость против течения:
120/20=6 км/час
Найдем скорость течения реки:
(10-6):2=2 км/час
Найдем скорость лодки:
10-2 = 6+2 = 8 км/час
Ответ: 8 км/ч собственная скорость лодки.

Answer 2

Пусть х скорость лодки, а у скорость течения тогда получим систему уравнений
{120/(х+у)=12
{120/(х-у)=20

{120=12х+12у
{120=20х-20у

{10=х+у
{30=5х-5у

Из первого
У=10-х

Во второе Подставим
30=5х-5(10-х)
30=5х-50+5х
10х=80
Х=8км/ч
Скорость течения у=10-8=2км/час
Ответ скорость лодки 8 км /час

Answer 3

Problem Analysis

We are given that a boat traveled from point A to point B, a distance of 120 km, downstream in 12 hours. On the return trip, the boat took 20 hours. We need to find the speed of the boat.

Solution

Let's assume the speed of the boat in still water is x km/h, and the speed of the river current is y km/h.

When the boat is traveling downstream, it benefits from the speed of the river current, so its effective speed is (x + y) km/h. The time taken to travel from A to B downstream is 12 hours.

On the return trip, the boat is traveling against the current, so its effective speed is (x - y) km/h. The time taken to travel from B to A upstream is 20 hours.

We can set up two equations based on the given information:

Equation 1: 120 = (x + y) * 12 (downstream trip) Equation 2: 120 = (x - y) * 20 (upstream trip)

We can solve these equations to find the values of x and y.

Solving the Equations

Let's solve Equation 1 for x + y: ``` (x + y) * 12 = 120 x + y = 120 / 12 x + y = 10 ```

Let's solve Equation 2 for x - y: ``` (x - y) * 20 = 120 x - y = 120 / 20 x - y = 6 ```

Now we have a system of equations: ``` x + y = 10 x - y = 6 ```

We can solve this system of equations using the method of substitution or elimination.

Let's solve it using the method of elimination. We'll add the two equations together: ``` (x + y) + (x - y) = 10 + 6 2x = 16 x = 16 / 2 x = 8 ```

Now that we have the value of x, we can substitute it back into one of the original equations to find the value of y. Let's use Equation 1: ``` 8 + y = 10 y = 10 - 8 y = 2 ```

Therefore, the speed of the boat in still water is 8 km/h, and the speed of the river current is 2 km/h.

Answer

The speed of the boat in still water is 8 km/h.