Question

Два автомобиля вышли одновременно из точки А до точки В расстояние между которыми 930 км, скорость первого на 31 км/ч больше Чем у второго , и он прибыл в пункт В на 5 часов раньше Найдите скорость первого автомобиля

Answer 1

X - скорость первого автомобиля
х+31 - скорость второго
930/х - время в пути первого автомобиля
930/(х+31) - время в пути второго автомобиля
Получим уравнение для разницы во времени:
$\frac{930}{x}- \frac{930}{x+31}=5$ 
$930(x+31)-930x=5x(x+31)$ 
$930x+27900-930x=5 x^{2}+155x$ 
$5 x^{2} +155x-27900=0$ 
$D= 155^{2}+4*5*27900=582025$ 
$x_{1} = \frac{-155+ \sqrt{582025} }{2*5} =61$ 
$x_{2} = \frac{-155- \sqrt{582025} }{2*5} =-92$
Второй корень в квадратном уравнении является посторонним (т.к. он отрицательный и его значение нас не устраивает)
Ответ: скорость первого автомобиля примерно 61 км/ч

Answer 2

Problem Analysis

We are given that two cars start simultaneously from point A and travel to point B, which is a distance of 930 km away. The speed of the first car is 31 km/h greater than the speed of the second car. The first car arrives at point B 5 hours 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. Since the speed of the first car is 31 km/h greater, the speed of the first car can be represented as x + 31 km/h.

We know that the time taken by the first car to travel from A to B is 5 hours less than the time taken by the second car. Let's represent the time taken by the second car as t hours. Therefore, the time taken by the first car is t - 5 hours.

We can use the formula speed = distance / time to calculate the speeds of the two cars.

For the second car: x = 930 / t km/h

For the first car: x + 31 = 930 / (t - 5) km/h

Now, we can solve these two equations to find the value of x, which represents the speed of the second car.

Calculation

Let's solve the equations:

Equation 1: x = 930 / t

Equation 2: x + 31 = 930 / (t - 5)

We can substitute Equation 1 into Equation 2:

930 / t + 31 = 930 / (t - 5)

To simplify the equation, we can cross-multiply:

930(t - 5) + 31t = 930t

Expanding and simplifying:

930t - 4650 + 31t = 930t

Combining like terms:

961t - 4650 = 930t

Moving the terms to one side:

961t - 930t = 4650

Simplifying:

31t = 4650

Dividing both sides by 31:

t = 150

Now that we have the value of t, we can substitute it back into Equation 1 to find the speed of the second car:

x = 930 / t = 930 / 150 = 6.2 km/h

Therefore, the speed of the second car is 6.2 km/h.

Since the speed of the first car is 31 km/h greater, the speed of the first car is:

x + 31 = 6.2 + 31 = 37.2 km/h

Therefore, the speed of the first car is 37.2 km/h.

Answer

The speed of the first car is 37.2 km/h.