Question

Решите задачу, выделяя три этапа математического моделирования. Учащиеся решили совершить поход к истоку реки Волга. Сначала они ехали на поезде, затем на автобусе и, наконец, шли пешком, преодолев в общей сложности 224 км. Путь, который дети проехали на автобусе, оказалось на 28 км длиннее, чем путь, пройденный пешком, и составил 1/5 части пути преодолённого на поезде. Найдите протяжённость участка пути, которые учащиеся шли пешком. Прошу помогите!!!

Answer 1

Х км -  путь, пройденный пешком.
(х+28) км - путь, проделанный на автобусе.
224-х-(х+28)=196-2х  км - путь, проделанный на поезде

$\frac{1}{5}(196-2x)=x+28\\\\196-2x=5x+140\\\\7x=56\\\\x=8$

Answer 2

Mathematical Modeling of the Students' Trip

To solve the problem of finding the distance the students walked, we can break down the mathematical modeling into three main steps:

1. Defining Variables and Formulating Equations: - Let's denote the distance traveled by train as x km, the distance traveled by bus as y km, and the distance traveled on foot as z km. - We are given that the total distance traveled is 224 km, so we have the equation: x + y + z = 224. - We also know that the distance traveled by bus is 28 km longer than the distance traveled on foot, which gives us the equation: y = z + 28. - Additionally, the distance traveled by bus is 1/5 of the distance traveled by train, so we have the equation: y = (1/5)x.

2. Solving the Equations: - We can use the system of equations to solve for the values of x, y, and z.

3. Verifying the Solution: - After obtaining the values of x, y, and z, we can verify that they satisfy all the given conditions in the problem.

Solution Steps

1. Defining Variables and Formulating Equations: - Let's denote the distance traveled by train as x km, the distance traveled by bus as y km, and the distance traveled on foot as z km. - The total distance traveled is 224 km, so we have the equation: x + y + z = 224. - The distance traveled by bus is 28 km longer than the distance traveled on foot, which gives us the equation: y = z + 28. - The distance traveled by bus is 1/5 of the distance traveled by train, so we have the equation: y = (1/5)x.

2. Solving the Equations: - We can solve the system of equations to find the values of x, y, and z.

3. Verifying the Solution: - After obtaining the values of x, y, and z, we can verify that they satisfy all the given conditions in the problem.

Let's proceed with solving the system of equations to find the distance the students walked.