Question

Из А в В одновременно выехали два автомобиля.Первый проехал с постоянной скоростью весь путь.Второй проехал первую половину пути со скоростью 7-км/ч, а вторую половину пути проехал со скоростью на 21 км/ч больше скорости первого, в результате чего прибыл в В одновременно с первым автомобилем.Найдите скорость первого автомобиля.

Answer 1

Х скорость первого автомобиля
у половина всего пути
время первого на весь путь:  2у/х
время второго на первую половину пути:  у/70,
на вторую половину пути: у/(х+21)
время второго на весь путь: у/70 + у/(х+21)=у(х+91)/(70х+1470)
приравняем время первого и второго автомобиля
2у/х=у(х+91)/(70х+1470)
2*(70х+1470)=х*(х+91)
140х+2940=х²+91х
х²-49х-2940=0
D=(-49)²-4*(-2940)=2401+11760=14161=119²
х=(49+119)/2=168/2=84
(второй корень отрицательный, он нам не нужен)
ответ: 84

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 travels the entire distance at a constant speed, while the second car travels the first half of the distance at a speed of 7 km/h and the second half at a speed 21 km/h faster than the speed of the first car. We need to find the speed of the first car.

Solution

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

The first car travels the entire distance at a constant speed, so the time taken by the first car is given by:

time taken by first car = d / speed of first car

The second car travels the first half of the distance at a speed of 7 km/h, so the time taken by the second car for the first half of the distance is:

time taken by second car for first half = (d/2) / 7

The second car travels the second half of the distance at a speed 21 km/h faster than the speed of the first car. Let's assume the speed of the first car is x km/h. So, the speed of the second car for the second half of the distance is (x + 21) km/h. Therefore, the time taken by the second car for the second half of the distance is:

time taken by second car for second half = (d/2) / (x + 21)

Since both cars arrive at point B simultaneously, the total time taken by both cars is the same. Therefore, we can equate the time taken by the first car to the sum of the times taken by the second car for the first and second halves of the distance:

d / speed of first car = (d/2) / 7 + (d/2) / (x + 21)

Now, we can solve this equation to find the value of x, which represents the speed of the first car.

Calculation

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

d / x = (d/2) / 7 + (d/2) / (x + 21)

Multiplying both sides of the equation by 2x(x + 21) to eliminate the denominators:

2d(x + 21) = dx + 2d(7)

Expanding and simplifying the equation:

2dx + 42d = dx + 14d

Rearranging the equation:

dx = 28d

Dividing both sides of the equation by d:

x = 28

Therefore, the speed of the first car is 28 km/h.

Answer

The speed of the first car is 28 km/h.