Question

Машина ехала по шоссе 3 час, по проселочной дороге - 2 часа. Скорость по проселочной дороге была на 15 км/ч меньше, чем по шоссе. Общее расстояние, которое проехала машина - 270 км. Надо узнать с какой скоростью двигалась машина по шосее и по проселочной догоре. Нужны два способа решения

Answer 1

3(х+15)+ 2х=270

5х+45=270

5х=225

х=45 км/ч по просел

 

45+15=60км/ч по шоссе

Answer 2

Problem Analysis

To find the speed at which the car was traveling on the highway and on the dirt road, we need to solve a system of equations. Let's denote the speed on the highway as x km/h and the speed on the dirt road as y km/h. We are given the following information:

- The car traveled on the highway for 3 hours. - The car traveled on the dirt road for 2 hours. - The speed on the dirt road was 15 km/h less than the speed on the highway. - The total distance traveled by the car was 270 km.

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

1. Equation 1: 3x (distance on the highway) + 2y (distance on the dirt road) = 270 km 2. Equation 2: y = x - 15 (speed on the dirt road is 15 km/h less than the speed on the highway)

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

Solution 1: Substitution Method

We can solve the system of equations using the substitution method. Let's solve Equation 2 for y and substitute it into Equation 1:

Equation 1: 3x + 2(x - 15) = 270

Simplifying Equation 1:

3x + 2x - 30 = 270

5x - 30 = 270

5x = 300

x = 60

Substituting the value of x back into Equation 2 to find y:

y = 60 - 15

y = 45

Therefore, the car was traveling at a speed of 60 km/h on the highway and 45 km/h on the dirt road.

Solution 2: Elimination Method

We can also solve the system of equations using the elimination method. Let's multiply Equation 2 by 2 to make the coefficients of y in both equations the same:

Equation 1: 3x + 2y = 270

Equation 2: 2y = 2x - 30

Adding Equation 1 and Equation 2:

(3x + 2y) + (2x - 30) = 270 + (2x - 30)

Simplifying:

5x - 30 = 270 + 2x - 30

5x - 2x = 270

3x = 270

x = 90

Substituting the value of x back into Equation 2 to find y:

2y = 2(90) - 30

2y = 180 - 30

2y = 150

y = 75

Therefore, the car was traveling at a speed of 90 km/h on the highway and 75 km/h on the dirt road.

Summary

There are two ways to solve the problem:

1. Substitution Method: - The car was traveling at a speed of 60 km/h on the highway and 45 km/h on the dirt road.

2. Elimination Method: - The car was traveling at a speed of 90 km/h on the highway and 75 km/h on the dirt road.

Please let me know if you need any further assistance!