Question

Первые 280 км дороги из пункта А в пункт В автобус проехал с некоторой скоростью, а оставшиеся 480 км- со скоростью на 10 км/час большей. Найдите начальную скорость автобуса, если на весь путь из А в В он затратил 10 часов.

Answer 1

Обозначим первичную скорость автобуса через х и составим уравнение по условию задачи
$\frac{280}{x}+ \frac{480}{x+10}=10$
левую часть приведем к общему знаменателю
$\frac{280*(x+10)+480x}{x^2+10x}=10$
$\frac{280x+2800+480x}{x^2+10x}=10$
$\frac{760x+2800}{x^2+10x}=10$
умножим обе части уравнения на знаменатель
$760x+2800=10x^2+100x$
и в итоге получаем простое квадраное уравнение
$10x^2-660x-2800=0$
по формуле дискрименанта и корней находим первоначальную скорость
$D=b^2-4ac$
$x_1_,_2= \frac{-b+/- \sqrt{D} }{2a}$
получаем два корня $x_1=-4$  и $x_2=70$
очевидно, что для решения нашей задачи нас удовлетворяет только второй корень.
Ответ:первоначальная скорость автобуса 70 км/ч.

Answer 2

Problem Analysis

We are given that a bus traveled the first 280 km of a road from point A to point B at a certain speed, and then traveled the remaining 480 km at a speed that is 10 km/h faster. The total time taken for the entire journey from A to B is 10 hours. We need to find the initial speed of the bus.

Solution

Let's assume the initial speed of the bus is x km/h.

The time taken to travel the first 280 km at this speed is given by time1 = distance1 / speed1.

The time taken to travel the remaining 480 km at a speed that is 10 km/h faster is given by time2 = distance2 / speed2, where speed2 = (x + 10) km/h.

According to the given information, the total time taken for the entire journey is 10 hours. Therefore, we have the equation time1 + time2 = 10.

Substituting the values of distance1, distance2, speed1, and speed2 into the equation, we can solve for x.

Calculation

Let's calculate the value of x using the given information.

- distance1 = 280 km - distance2 = 480 km - speed1 = x km/h - speed2 = (x + 10) km/h - total time = 10 hours

Using the equation time1 + time2 = 10, we can substitute the values and solve for x.

time1 = distance1 / speed1 = 280 / x hours

time2 = distance2 / speed2 = 480 / (x + 10) hours

Substituting the values into the equation:

280 / x + 480 / (x + 10) = 10

To solve this equation, we can multiply through by x(x + 10) to eliminate the denominators:

280(x + 10) + 480x = 10x(x + 10)

Simplifying the equation:

280x + 2800 + 480x = 10x^2 + 100x

Combining like terms:

760x + 2800 = 10x^2 + 100x

Rearranging the equation to form a quadratic equation:

10x^2 - 660x + 2800 = 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, where a = 10, b = -660, and c = 2800.

Substituting the values into the formula:

x = (-(-660) ± sqrt((-660)^2 - 4 * 10 * 2800)) / (2 * 10)

Simplifying the equation:

x = (660 ± sqrt(435600 - 112000)) / 20

x = (660 ± sqrt(323600)) / 20

x = (660 ± 568.18) / 20

Solving for x:

x1 = (660 + 568.18) / 20 = 62.908 km/h

x2 = (660 - 568.18) / 20 = 5.191 km/h

Since the speed of the bus cannot be negative, the initial speed of the bus is 62.908 km/h.

Answer

The initial speed of the bus is 62.908 km/h.