Question

Велосипедист ехал 2 ч по лесной дороге и 1 ч по шоссе, всего он проехал 40 км. Скорость его на шоссе была на 4 км/ч больше, чем скорость на лесной дороге. С какой скоростью велосипедист ехал по шоссе, и с какой по лесной дороге? Пожалуйста решите с помощью системы линейных уравнений(способ сложения).

Answer 1

Если х–скорость по лесной дороге, то х+4 – по шоссе
2х+(х+4)=40
3х=36
х=12км/ч – скорость по лесной дороге
х+4=12+4= 16км/ч – скорость по шоссе

Answer 2

Problem Analysis

We are given that a cyclist traveled for 2 hours on a forest road and 1 hour on a highway, covering a total distance of 40 km. The speed on the highway was 4 km/h faster than the speed on the forest road. We need to find the speed of the cyclist on the highway and on the forest road.

Solution

Let's assume the speed of the cyclist on the forest road is x km/h. Then the speed on the highway would be x + 4 km/h.

We can use the formula distance = speed × time to create two equations based on the given information:

1. Forest road equation: 2x = distance on forest road 2. Highway equation: 1(x + 4) = distance on highway

We know that the total distance covered is 40 km, so we can write another equation:

3. distance on forest road + distance on highway = 40

Now we can solve this system of equations to find the values of x and x + 4.

Solving the System of Equations

Let's solve the system of equations using the method of substitution.

From equation 1, we have 2x = distance on forest road. We can rewrite this as x = (distance on forest road) / 2.

Substituting this value of x in equation 2, we get 1((distance on forest road) / 2 + 4) = distance on highway.

Simplifying this equation, we have (distance on forest road) / 2 + 4 = distance on highway.

Now, we can substitute the value of distance on highway from equation 3, which is 40 - (distance on forest road).

Substituting this value in the equation above, we get (distance on forest road) / 2 + 4 = 40 - (distance on forest road).

Simplifying further, we have (distance on forest road) / 2 + (distance on forest road) = 40 - 4.

Combining like terms, we get (3/2) × (distance on forest road) = 36.

Multiplying both sides by 2/3, we get distance on forest road = (2/3) × 36.

Simplifying, we find distance on forest road = 24.

Now, we can substitute this value in equation 1 to find the speed on the forest road:

2x = 24.

Simplifying, we get x = 12.

Therefore, the speed of the cyclist on the forest road is 12 km/h.

To find the speed on the highway, we can substitute this value of x in equation 2:

1(x + 4) = distance on highway.

Substituting the value of x, we get 1(12 + 4) = distance on highway.

Simplifying, we find 16 = distance on highway.

Therefore, the speed of the cyclist on the highway is 16 km/h.

Answer

The cyclist traveled at a speed of 12 km/h on the forest road and 16 km/h on the highway.