Question

Первый автомобиль весь путь может пройти за 12 часов, второй – за 10 часов. Через 7 часов расстояние между ними 136 км. Найти расстояние и скорость каждого.

Answer 1

Х-скорость первого автомобиля
у - скорость второго автомобиля , из условия задачи имеем
12х = 10у        у =12х/10 = 1,2х  Подставим значение у во второе уравнение
(у - х) *7 = 136    (1,2 х - х)*7 = 136       1,4х =136     х =  97,1 км/ч
Скорость второго автомобиля  равна = 97,1*1,2  = 116,5 км/ч  
Весь путь равен =10у = 10 * 116,5 = 1165 км  
 

Answer 2

Problem Analysis

We are given two cars that can travel a certain distance in different amounts of time. After 7 hours, the distance between them is 136 km. We need to find the distance and speed of each car.

Solution

Let's assume that the first car's speed is x km/h and the second car's speed is y km/h. We can use the formula distance = speed * time to find the distance traveled by each car.

After 7 hours, the first car has traveled a distance of 7x km, and the second car has traveled a distance of 7y km. The difference between these distances is 136 km.

So, we have the equation: 7x - 7y = 136.

We also know that the first car takes 12 hours to travel the entire distance, and the second car takes 10 hours. Therefore, the distance traveled by each car can be expressed as:

Distance traveled by the first car = 12x km Distance traveled by the second car = 10y km

We can now solve these equations to find the values of x and y.

Calculation

Let's solve the equation 7x - 7y = 136 for x:

7x - 7y = 136 x - y = 136/7

Simplifying further, we get:

x - y = 19.43

Now, let's solve the equations 12x = distance and 10y = distance for the distance traveled by each car:

12x = distance 10y = distance

Substituting the value of distance from the first equation into the second equation, we get:

10y = 12x

Simplifying further, we get:

5y = 6x

Now, we have a system of equations:

x - y = 19.43 5y = 6x

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

Solution

Solving the system of equations, we find that:

x = 29.145 km/h y = 24.2875 km/h

Therefore, the first car's speed is approximately 29.145 km/h and the second car's speed is approximately 24.2875 km/h.

To find the distance traveled by each car, we can substitute these values back into the equations:

Distance traveled by the first car = 12x = 12 * 29.145 = 349.74 km Distance traveled by the second car = 10y = 10 * 24.2875 = 242.875 km

Therefore, the first car travels approximately 349.74 km and the second car travels approximately 242.875 km.

Summary

The first car travels approximately 349.74 km at a speed of 29.145 km/h, while the second car travels approximately 242.875 km at a speed of 24.2875 km/h.