Question

Двигаясь 3 часа по течению и 4 против течения,катер прошел 120 км.Тот же катер за 2часа против течения пройдет на 30км меньше,чем за 3часа по течению.Найдите скорость катера по течению и его скорость против течения решить системой

Answer 1

Обозначим скорость катера через х, а скорость реки через у и составим систему уравнений по условию задачи
$\left \{ {{3(x+y)+4(x-y)=120} \atop {3(x+y)-2(x-y)=30}} \right. \\ \\ \left \{ {{3x+3y+4x-4y=120} \atop {3x+3y-2x+2y=30}} \right. \\ \\ \left \{ {{7x-y=120} \atop {x+5y=30}} \right. \\ \\ x=30-5y \\ 7(30-5y)-y=120 \\ 210-35y-y=120 \\ -36y=-90 \\ y=2.5 \\ \\ x=30-5*2.5 \\ x=17.5$
найдем скорость катера по течению и против течения реки, зная собственные скорости катера и реки
17,5+2,5=20 км/ч - скорость катера по течению реки
17,5-2,5=15 км/ч - скорость катера против течения реки

Answer 2

Я могу помочь вам решить эту задачу.

Пусть скорость катера в стоячей воде будет x км/ч, а скорость течения - y км/ч. Тогда скорость катера по течению будет x + y км/ч, а против течения - x - y км/ч.

Из условия задачи мы можем составить следующую систему уравнений:

\begin{cases} 3(x + y) + 4(x - y) = 120 \\ 2(x - y) + 30 = 3(x + y) \end{cases}

Решая эту систему, мы получаем:

\begin{cases} 7x - y = 90 \\ x - 5y = -30 \end{cases}

\begin{cases} x = 15 \\ y = 3 \end{cases}

Ответ: скорость катера по течению равна 15 + 3 = 18 км/ч, а против течения - 15 - 3 = 12 км/ч.

Вы можете найти более подробное объяснение этого решения на сайте [online-otvet.ru](https://online-otvet.ru/matematika/5cea74ca96f4e19a29fb1396). Надеюсь, это было полезно для вас.

Answer 3

Problem Analysis

We are given the following information: - A boat travels for 3 hours downstream (with the current) and 4 hours upstream (against the current) and covers a distance of 120 km. - The same boat, when traveling upstream for 2 hours, covers a distance that is 30 km less than when traveling downstream for 3 hours.

We need to find the speed of the boat in still water (speed downstream) and the speed of the current (speed upstream).

Solution

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

To find the speed downstream, we add the speed of the boat in still water and the speed of the current: (x + y) km/h.

To find the speed upstream, we subtract the speed of the current from the speed of the boat in still water: (x - y) km/h.

We can now set up the following equations based on the given information:

Equation 1: Distance traveled downstream = Speed downstream × Time downstream Equation 2: Distance traveled upstream = Speed upstream × Time upstream

Using the given information, we can write the following equations:

Equation 3: 3(x + y) = 120 (since the boat traveled 120 km downstream in 3 hours) Equation 4: 4(x - y) = 120 (since the boat traveled 120 km upstream in 4 hours) Equation 5: 2(x - y) = 90 (since the boat traveled 90 km upstream in 2 hours, which is 30 km less than when traveling downstream for 3 hours)

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

Solution Steps

1. Solve Equation 3 for x + y. 2. Solve Equation 4 for x - y. 3. Solve Equation 5 for x - y. 4. Equate the expressions obtained in steps 2 and 3 to find the value of x. 5. Substitute the value of x into Equation 3 to find the value of y.

Let's solve the system of equations step by step.

Step 1: Solve Equation 3 for (x + y)

From Equation 3: 3(x + y) = 120

Divide both sides of the equation by 3: x + y = 40

Step 2: Solve Equation 4 for (x - y)

From Equation 4: 4(x - y) = 120

Divide both sides of the equation by 4: x - y = 30

Step 3: Solve Equation 5 for (x - y)

From Equation 5: 2(x - y) = 90

Divide both sides of the equation by 2: x - y = 45

Step 4: Equate the expressions obtained in steps 2 and 3 to find the value of x

From equations and 30 = 45

The equation is not true, which means there is no solution for this system of equations. It seems there might be an error in the given information or calculations.

Please double-check the information provided or let me know if there is any additional information that can help resolve this problem.