Question

Два автобуса отправились одновременно из одного села в другое, расстояние между которыми равно 36 к. Первый автобус прибыл в назначенный пункт на 15 минут раньше второго автобуса, скорость которого была меньше скорости первого автобуса на 2 км/ч.ВЫЧИСЛИТЕ скорость каждого автобуса.

Answer 1

Х км/ч - скорость медленного автобуса
х+2 км/ч - скорость быстрого автобуса
$\frac{36}{x}$ ч - время в пути медленного автобуса
$\frac{36}{x+2}$ ч - время в пути быстрого автобуса
Разница во времени 15 мин = $\frac{1}{4}$ ч.
$\frac{36}{x}-\frac{36}{x+2}= \frac{1}{4}\\ x \neq 0,\ x \neq -2\\ 144x+288-144x=x^2+2x\\ x^2+2x-288=0\\ D=1156\\ x= \frac{-2 \pm 34}{2} \\ x_1=-18,\ x_2=16$
x=-18 км\ч - не удловл.условию
Значит, 16 км/ч - скорость медленного автобуса
16+2=18 км/ч - скорость быстрого автобуса
Ответ 16 км/ч, 18 км/ч.

Answer 2

Problem Analysis

We are given that two buses start simultaneously from one village to another, with a distance of 36 km between them. The first bus arrives at the destination 15 minutes earlier than the second bus, and the second bus has a speed 2 km/h slower than the first bus. We need to calculate the speed of each bus.

Solution

Let's assume the speed of the first bus is x km/h. Then the speed of the second bus will be x - 2 km/h.

We can use the formula speed = distance / time to calculate the time taken by each bus to travel the distance of 36 km.

The time taken by the first bus is given by 36 / x hours.

The time taken by the second bus is given by 36 / (x - 2) hours.

We are given that the first bus arrives 15 minutes earlier than the second bus. Since 15 minutes is equal to 0.25 hours, we can set up the following equation:

36 / x = 36 / (x - 2) + 0.25

To solve this equation, we can cross-multiply and simplify:

36(x - 2) = 36x + 0.25x(x - 2)

Simplifying further:

36x - 72 = 36x + 0.25x^2 - 0.5x

Combining like terms:

0.25x^2 - 0.5x - 72 = 0

Now we have a quadratic equation. We can solve it using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, the values of a, b, and c are:

a = 0.25 b = -0.5 c = -72

Plugging these values into the quadratic formula, we can calculate the value of x.

Let's calculate the value of x using the quadratic formula:

x = (-(-0.5) ± √((-0.5)^2 - 4 * 0.25 * -72)) / (2 * 0.25)

Simplifying further:

x = (0.5 ± √(0.25 + 72)) / 0.5

x = (0.5 ± √(72.25)) / 0.5

x = (0.5 ± 8.5) / 0.5

Now we have two possible values for x:

x1 = (0.5 + 8.5) / 0.5 = 18 x2 = (0.5 - 8.5) / 0.5 = -16

Since speed cannot be negative, we discard the value of x2.

Therefore, the speed of the first bus (x) is 18 km/h, and the speed of the second bus (x - 2) is 16 km/h.

Answer

The speed of the first bus is 18 km/h, and the speed of the second bus is 16 km/h.