Question

Расстояние между городами А и В равно 630 км. Из города В в город А выехал автобус со скоростью 40 км/ч. А через 3 часа из города А в город В выехал другой автобус со скоростью 45км/ч. На каком расстоянии от каждого города автобусы встретятся? Через какое время после после начала движения второго автобусы это произойдёт?

Answer 1

40 * 3 = 120км - проехал 1-ый автобус за 3 часа.
630 - 120 = 510 км - было между автобусами через 3 часа.
40 + 45 = 85 км/ч - скорость сближения.
510 : 85 = через 6 часов они встретятся.
40 * 6 +120 = 360 км - от города В произойдёт встреча
630 - 360 = 270 км - от города А произойдёт встреча.

Answer 2

Problem Analysis

We are given that the distance between cities A and B is 630 km. An initial bus starts from city B to city A with a speed of 40 km/h. After 3 hours, another bus starts from city A to city B with a speed of 45 km/h. We need to find the distance from each city where the buses will meet and the time it will take for the second bus to reach that point.

Solution

Let's assume that the buses meet at a distance x km from city A. Since the total distance between the two cities is 630 km, the distance from city B to the meeting point will be (630 - x) km.

To find the time it takes for the first bus to reach the meeting point, we can use the formula:

Time = Distance / Speed

For the first bus: Time taken = (630 - x) / 40

For the second bus: Time taken = x / 45

Since the total time taken by both buses is 3 hours, we can write the equation:

(630 - x) / 40 + x / 45 = 3

Simplifying the equation, we get:

(630 - x) * 45 + x * 40 = 3 * 40 * 45

Now, we can solve this equation to find the value of x.

Calculation

Let's solve the equation to find the value of x.

(630 - x) * 45 + x * 40 = 3 * 40 * 45

Simplifying the equation:

28350 - 45x + 40x = 5400

Combining like terms:

-5x + 28350 = 5400

Moving the constant term to the other side:

-5x = 5400 - 28350

-5x = -22950

Dividing both sides by -5:

x = -22950 / -5

x = 4590

Answer

The buses will