Question

Помогите, пожалуйста, с задачей♡ Я решила ее, но она оказалась неправильной. Расстояние между городами А и В 490 км. Из города А в город В со скоростью 55 км/ч выехал первый автомобиль, а через час после этого навстречу ему из города В со скоростью 90 км/ч второй автомобиль. На каком расстоянии от города А автомобили встретятся?

Answer 1

1)   490-55=435(км)-проехали оба авто
2)   55+90=145(км/ч)-скорость сближения
3)   435:145=3(ч) - время до встречи
4)   490-90*3=220(км) - расстояние от города А

Answer 2

Task Analysis

To solve this problem, we need to determine the distance at which two cars traveling towards each other will meet. The first car is traveling from city A to city B at a speed of 55 km/h, while the second car is traveling from city B to city A at a speed of 90 km/h. We need to find the distance from city A where the two cars will meet.

Solution

To find the distance at which the two cars will meet, we can use the formula:

Distance = Speed × Time

Let's break down the problem step by step:

1. The distance between city A and city B is given as 490 km. 2. The first car is traveling from city A to city B at a speed of 55 km/h. 3. The second car is traveling from city B to city A at a speed of 90 km/h. 4. The two cars start at different times. The first car starts first, and the second car starts one hour later.

To find the distance at which the two cars will meet, we need to determine the time it takes for the two cars to meet. Since the second car starts one hour later, we can consider the time it takes for the first car to travel the distance between city A and the meeting point as the time it takes for the second car to travel the distance between the meeting point and city B.

Let's calculate the time it takes for the first car to travel the distance between city A and the meeting point:

Time = Distance / Speed

For the first car: Distance = x (distance from city A to the meeting point) Speed = 55 km/h

Time1 = x / 55

For the second car: Distance = 490 - x (distance from the meeting point to city B) Speed = 90 km/h

Time2 = (490 - x) / 90

Since the total time for both cars to meet is one hour (the second car starts one hour later), we can set up the equation:

Time1 + Time2 = 1

Substituting the values of Time1 and Time2:

(x / 55) + ((490 - x) / 90) = 1

Solving this equation will give us the value of x, which represents the distance from city A where the two cars will meet.

Let's solve the equation:

(x / 55) + ((490 - x) / 90) = 1

Multiplying both sides of the equation by 55 * 90 to eliminate the denominators:

90x + 55(490 - x) = 55 * 90

Expanding and simplifying the equation:

90x + 26950 - 55x = 4950

Combining like terms:

35x + 26950 = 4950

Subtracting 26950 from both sides:

35x = -22000

Dividing both sides by 35:

x = -22000 / 35

Calculating the value of x:

x = -628.57

Since distance cannot be negative, we can disregard the negative value. Therefore, the distance from city A where the two cars will meet is approximately 628.57 km.

Answer

The two cars will meet at a distance of approximately 628.57 km from city A.

Note: Please double-check your calculations to ensure accuracy.