Question

Из двух городов A и B выходят одновременно два автомобиля и встречаются через 5 ч. Скорость автомобиля, выходящего из A, на 10 км/ч меньше скорости другого автомобиля. Если бы первый автомобиль вышел из A на 4 ч. раньше второго, то встреча произошла бы в 150 км от B. Найдите РАССТОЯНИЕ между городами A и B.

Answer 1

Примерно такое решение

Answer 2

Problem Analysis

We are given that two cars, one starting from city A and the other from city B, meet after 5 hours. The car from city A is traveling 10 km/h slower than the other car. If the first car had started 4 hours earlier than the second car, they would have met 150 km from city B. We need to find the distance between cities A and B.

Solution

Let's assume the speed of the car starting from city A is x km/h and the speed of the car starting from city B is y km/h.

From the given information, we can form the following equations:

1. When the cars meet after 5 hours: - Distance traveled by the car from city A = 5x km - Distance traveled by the car from city B = 5y km

2. If the first car had started 4 hours earlier than the second car and they met 150 km from city B: - Distance traveled by the car from city A = (5 + 4)x km - Distance traveled by the car from city B = (5 - 4)y km

We can set up the following equation using the above information:

(5 + 4)x - (5 - 4)y = 150

Simplifying the equation, we get:

9x + 9y = 150

Dividing both sides of the equation by 9, we get:

x + y = 16.67

Since we know that the speed of the car from city A is 10 km/h slower than the speed of the car from city B, we can set up another equation:

x = y - 10

Substituting this value of x in the equation x + y = 16.67, we get:

(y - 10) + y = 16.67

Simplifying the equation, we get:

2y - 10 = 16.67

Adding 10 to both sides of the equation, we get:

2y = 26.67

Dividing both sides of the equation by 2, we get:

y = 13.33

Substituting this value of y in the equation x = y - 10, we get:

x = 13.33 - 10 = 3.33

Therefore, the speed of the car from city A is 3.33 km/h and the speed of the car from city B is 13.33 km/h.

To find the distance between cities A and B, we can use the formula:

Distance = Speed × Time

Since the cars meet after 5 hours, the distance between cities A and B is:

Distance = Speed × Time = 13.33 km/h × 5 h = 66.65 km

Therefore, the distance between cities A and B is approximately 66.65 km.

Answer

The distance between cities A and B is approximately 66.65 km.