Question

Из двух городов, расстояние между которыми 45 км, одновременно в одном направлении выехали автомобиль догоняет второй. Через сколько часов расстояние между автомобилями будет равно 10 км? Почему задача имеет два решеия

Answer 1

Пусть через х часов первый не доедет до второго 10 км.Он проедет 70х км и окажется в А, т.е не доедет до В 10 км. А второй проедет 60х км и окажется в В. АВ=10.Учитывая первоначальное расстояние между ними,получится уравнение:
70х+10=45+60х
70х-60х=45-10
10х=35
х=3,5 часа.

Пусть через х часов первый не доедет до второго 10 км.Он проедет 70х км и окажется в А, т е. проедет после В 10 км. Второй проедет 60х км и окажется в В. ВА=10.
Учитывая первоначальное расстояние между ними,получится уравнение: 
70х=45+60х+10
70х-60х=55
10х=55
х=5,5

Первое решение:первый автомобиль не догонит второй, не доедет до второго 10км. Т.е.  второй будет дальше первого на 10 км.

Второе решение:первый автомобиль перегонит второй и проедет ещё 10 км после обгона.

Answer 2

Problem Analysis

We have two cars that start from two different cities and are traveling towards each other. The distance between the cities is 45 km. One car starts chasing the other. We need to determine how many hours it will take for the distance between the cars to be 10 km.

Solution

Let's assume that the first car starts chasing the second car. We can set up an equation to represent the situation.

Let: - x be the time in hours it takes for the distance between the cars to be 10 km. - d1 be the distance traveled by the first car in x hours. - d2 be the distance traveled by the second car in x hours.

Since the first car is chasing the second car, the distance traveled by the first car will be greater than the distance traveled by the second car. Therefore, we can set up the following equation:

d1 = d2 + 10

We also know that the sum of the distances traveled by both cars is equal to the total distance between the cities, which is 45 km:

d1 + d2 = 45

Now we can solve these two equations to find the value of x.

Solving the Equations

To solve the equations, we can use the method of substitution. We can rearrange the first equation to solve for d1:

d1 = d2 + 10

Substituting this value of d1 into the second equation, we get:

(d2 + 10) + d2 = 45

Simplifying the equation:

2d2 + 10 = 45

Subtracting 10 from both sides:

2d2 = 35

Dividing both sides by 2:

d2 = 17.5

Now we can substitute this value of d2 back into the first equation to find d1:

d1 = 17.5 + 10 = 27.5

Therefore, the first car travels a distance of 27.5 km and the second car travels a distance of 17.5 km in x hours.

Answer

The distance between the cars will be 10 km after approximately 27.5 km traveled by the first car and 17.5 km traveled by the second car. The time it takes for this to happen is x hours.

Please note that the problem has two solutions because the cars can either meet when the first car is ahead of the second car or when the second car is ahead of the first car. The solution we obtained assumes that the first car is chasing the second car.