Question

Помогите пожалуйста. Надо решить СИСТЕМОЙ ИЗ ДВУХ УРАВНЕНИЙ.1) Собственная скорость моторной лодки больше скорости течения в 4 раза. Найдите скорость лодки по течению если , если за 1 час против течения и за 1/3 (дробь) часа по течению лодка пройдет 14 км.2) Дачник проделал путь длиной 46 километров . Он шел 2 часа пешком и 3 часа ехал на велосипеде . На велосипеде он двигался в 2,4 раза быстрее , чем пешком . С какой скоростью дачник шел и с какой скоростью ехал?

Answer 1

2)V-cкорость пешехода V1скорость велосипеда..

Получаем первое уравнение:2V=3V1=46

Решаем подставляем значение V1 2V+3*2,4*V=46

Отсюда V=5 a V1=12

Answer 2

Problem 1: Speed of a Motorboat in Relation to the Current

To solve this problem, we need to find the speed of the motorboat in relation to the current. Let's break down the given information:

- The speed of the motorboat is 4 times greater than the speed of the current. - The boat travels 14 km in 1 hour against the current. - The boat travels the same distance of 14 km in 1/3 hour with the current.

To find the speed of the motorboat, we can set up a system of equations.

Let's assume: - The speed of the motorboat is represented by x km/h. - The speed of the current is represented by y km/h.

Equation 1: The speed of the motorboat is 4 times greater than the speed of the current. ``` x = 4y ```

Equation 2: The boat travels 14 km in 1 hour against the current. ``` x - y = 14/1 = 14 ```

Equation 3: The boat travels 14 km in 1/3 hour with the current. ``` x + y = 14/(1/3) = 14 * 3 = 42 ```

Now we have a system of equations: ``` x = 4y (Equation 1) x - y = 14 (Equation 2) x + y = 42 (Equation 3) ```

To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of elimination.

Adding Equation 2 and Equation 3 eliminates the variable x: ``` (x - y) + (x + y) = 14 + 42 2x = 56 x = 56/2 x = 28 ```

Now we can substitute the value of x back into Equation 1 to find the value of y: ``` 28 = 4y y = 28/4 y = 7 ```

Therefore, the speed of the motorboat is 28 km/h and the speed of the current is 7 km/h.

Problem 2: Speed of a Hiker and Bicyclist

To solve this problem, we need to find the speed of the hiker and the bicyclist. Let's break down the given information:

- The total distance traveled is 46 km. - The hiker walks for 2 hours. - The bicyclist rides for 3 hours. - The bicyclist's speed is 2.4 times faster than the hiker's speed.

Let's assume: - The speed of the hiker is represented by x km/h. - The speed of the bicyclist is represented by y km/h.

Equation 1: The total distance traveled is 46 km. ``` 2x + 3y = 46 ```

Equation 2: The bicyclist's speed is 2.4 times faster than the hiker's speed. ``` y = 2.4x ```

Now we have a system of equations: ``` 2x + 3y = 46 (Equation 1) y = 2.4x (Equation 2) ```

To solve this system of equations, we can substitute the value of y from Equation 2 into Equation 1.

Substituting 2.4x for y in Equation 1: ``` 2x + 3(2.4x) = 46 2x + 7.2x = 46 9.2x = 46 x = 46/9.2 x = 5 ```

Now we can substitute the value of x back into Equation 2 to find the value of y: ``` y = 2.4x y = 2.4(5) y = 12 ```

Therefore, the speed of the hiker is 5 km/h and the speed of the bicyclist is 12 km/h.

I hope this helps! Let me know if you have any further questions.