Question

Из А в В одновременно выехали два автомобиля. Первый проехал с постоянной скорость весь путь. Второй проехал первую половину пути со скоростью 30 км/ч, а вторую половину пути проехал со скоростью на 9 км/ч больше скорости первого, в результате чего прибыл в В одновременно с первым автомобилистом. Найдите скорость первого автомобилиста.

Answer 1

рассчитать общую скорость автомобиля умножь на общее время автомобиля найдешь общий путь

Answer 2

Problem Analysis

We are given that two cars, A and B, simultaneously start from point A and travel to point B. The first car, A, travels the entire distance at a constant speed. The second car, B, travels the first half of the distance at a speed of 30 km/h and the second half at a speed that is 9 km/h faster than the speed of the first car. We need to find the speed of the first car, A.

Solution

Let's assume the distance between points A and B is D km.

The first car, A, travels the entire distance at a constant speed, which we'll call V km/h. Therefore, the time taken by car A to travel from A to B is given by: Time taken by car A = D / V The second car, B, travels the first half of the distance at a speed of 30 km/h. Therefore, the time taken by car B to travel the first half of the distance is given by: Time taken by car B for the first half = (D/2) / 30 = D / 60 The second half of the distance is traveled by car B at a speed that is 9 km/h faster than the speed of car A. Therefore, the time taken by car B to travel the second half of the distance is given by: Time taken by car B for the second half = (D/2) / (V + 9) Since car B arrives at point B at the same time as car A, the total time taken by car B is equal to the time taken by car A. Therefore, we can write the equation: Time taken by car B = Time taken by car A

Substituting the values from equations and into equation we get: D / 60 + (D/2) / (V + 9) = D / V

Simplifying the equation, we get: 1/60 + 1 / (2(V + 9)) = 1 / V

To solve this equation, we can multiply through by the least common multiple of the denominators, which is 60V(V + 9). This gives us: V(V + 9) + 30V = 60(V + 9)

Expanding and simplifying the equation, we get: V^2 + 9V + 30V = 60V + 540 V^2 - 21V - 540 = 0

We can solve this quadratic equation to find the value of V.