Question

Решите задачу с помощью уравнения: Грузовой автомобиль проходит расстояние от села до города за 3 часа, а легковой - за два. Какова скорость легкового и грузового автомобилей, если известно, что скорость легкового автомобиля на 30 км/с больше скорости грузового?

Answer 1

30 километров в секунду? Если все таки в км/ч, то вот уравнение:

2(х+30)=3х

2х+60=3х

х=60

скорость грузового 60

скорость легкового 60+30=90

Answer 2

Solving the Problem Using Equations

To solve the problem of finding the speeds of the passenger and freight vehicles, we can use the equation of speed, which is distance divided by time.

Let's denote the speed of the freight vehicle as x km/h and the speed of the passenger vehicle as (x + 30) km/h (since the speed of the passenger vehicle is 30 km/h more than the speed of the freight vehicle).

The distance traveled by the freight vehicle is given as 3 hours, and the distance traveled by the passenger vehicle is given as 2 hours.

Using the equation of speed, we can set up the following equations:

1. For the freight vehicle: distance = speed × time So, distance = x × 3

2. For the passenger vehicle: distance = speed × time So, distance = (x + 30) × 2

By solving these equations, we can find the values of x and (x + 30), which represent the speeds of the freight and passenger vehicles, respectively.

Solution

To solve the equations, we can set the two distances equal to each other and solve for x:

x × 3 = (x + 30) × 2 3x = 2x + 60 3x - 2x = 60 x = 60

So, the speed of the freight vehicle (x) is 60 km/h.

Now, to find the speed of the passenger vehicle, we can substitute the value of x into the expression (x + 30):

60 + 30 = 90

So, the speed of the passenger vehicle (x + 30) is 90 km/h.

Therefore, the speed of the freight vehicle is 60 km/h and the speed of the passenger vehicle is 90 km/h.

This solution is based on the given information and the equations of speed, and it provides the speeds of both the freight and passenger vehicles.