Question

Два автомобиля выезжают одновременно из одного города в другой.Скорость первого на 20 км/ч больше скорости второго, поэтому первый автомобильприезжает на место на 2 ч. 24 мин. раньше второго. С какой скоростью шел первый автомобиль, если расстояние М/У городами 420 км.

Answer 1

Пусть х км/ч скорость второго авто, тогда (х+20) км/ч скорость первого. Замечаем, что 2 ч  24 мин = 2,4 ч , составляем уравнение по времени в пути двух авто: 420 / х  - 420 / (х+20)  = 2,4 Приводим к общему знаменателю х(х+20) иотбрасываем его, записав, что х не=0 и х не=-20 420(х+20)-420х=2,4х(х+20)420х+8400-420х = 2,4x^2+48х2,4x^2+48x- 8400 =0x^2+20x-3500=0D= 400+4*3500=14400, 2 корнях(1)=(-20+120)/2 = 50  (км/ч ) скорость второго автох(2)= (-20-120)/2= -70 не подходит под усл задачи 50+20=70 км/ч  скорость первого авто

Answer 2

Problem Analysis

We are given that two cars start simultaneously from one city to another. The first car is traveling at a speed 20 km/h faster than the second car. The first car arrives at the destination 2 hours and 24 minutes earlier than the second car. We need to find the speed of the first car.

Solution

Let's assume the speed of the second car is x km/h. Therefore, the speed of the first car would be x + 20 km/h.

We are also given that the distance between the cities is 420 km.

To find the speed of the first car, we can use the formula: time = distance / speed.

The time taken by the first car is the time taken by the second car minus 2 hours and 24 minutes. We need to convert this time into hours.

2 hours and 24 minutes is equal to 2 + 24/60 = 2.4 hours.

Using the formula, we can set up the equation:

420 / (x + 20) = 420 / x - 2.4

Now, let's solve this equation to find the value of x.

420 / (x + 20) = 420 / x - 2.4

Multiplying both sides by x(x + 20) to eliminate the denominators:

420x = 420(x + 20) - 2.4x(x + 20)

Simplifying the equation:

420x = 420x + 8400 - 2.4x^2 - 48x

Rearranging the equation:

2.4x^2 + 48x - 8400 = 0

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

Using the quadratic formula: x = (-b ± sqrt(b^2 - 4ac)) / 2a

For our equation, a = 2.4, b = 48, and c = -8400.

x = (-48 ± sqrt(48^2 - 4 * 2.4 * -8400)) / (2 * 2.4)

Simplifying further:

x = (-48 ± sqrt(2304 + 80640)) / 4.8

x = (-48 ± sqrt(82944)) / 4.8

x = (-48 ± 288) / 4.8

Now, we have two possible values for x. Let's calculate both:

x1 = (-48 + 288) / 4.8 = 240 / 4.8 = 50

x2 = (-48 - 288) / 4.8 = -336 / 4.8 = -70

Since speed cannot be negative, we discard the negative value of x.

Therefore, the speed of the second car is 50 km/h.

The speed of the first car is x + 20 = 50 + 20 = 70 km/h.

Answer

The first car was traveling at a speed of 70 km/h.