Question

Школьные Знания.com Задай вопрос из школьного предмета 5 - 9 классыАлгебра 5+3 б 3. В пункте О прямолинейного шоссе, не принадлежащем участку АВ этого шоссе, произошла авария. Пункт скорой помощи находится на середине участка АВ, в пункте М на расстоянии 9 км от места аварии. Определите длину участка АВ, если расстояние от пункта О до одного из концов участка АВ равно 1 4 длины этого участка. А. 8 км. Б. 10 км. В. 12 км. Г. 16 км.

Answer 1

Обозначим за половину отрезка AB x.
$x = \frac{1}{2}AB$
Тогда:
$x - 9 = \frac{1}{4} * 2x$, сократим в правой части на 2.
$x - 9 = \frac{1}{2}x$, разделим всё выражение на 2.
$2x - 18 = x$
$x = 18$

Весь путь от A до B:
2 * x = 2 * 18 = 36 км.

Answer 2

Problem Analysis

We are given that there has been an accident on a straight highway, and a first aid station is located in the middle of the section of the highway. Another point, M, is located 9 km away from the accident site. We need to determine the length of the section of the highway, AB, if the distance from point O to one of the ends of AB is equal to 1/4 of the length of AB.

Solution

Let's assume the length of the section AB is x km. According to the problem, the distance from point O to one of the ends of AB is equal to 1/4 of the length of AB. Therefore, the distance from O to either A or B is x/4 km.

Since point M is located 9 km away from the accident site, we can conclude that the distance from M to either A or B is (x - 9) km.

Now, let's analyze the given information: - Distance from O to either A or B: x/4 km - Distance from M to either A or B: (x - 9) km

Since the first aid station is located in the middle of the section AB, the distance from O to M is half the length of AB. Therefore, we can write the following equation:

(x/4) + (x - 9) = (x/2)

Simplifying the equation:

(x/4) + x - 9 = (x/2) (x/4) + (4x/4) - 9 = (x/2) (5x/4) - 9 = (x/2)

To solve for x, we can multiply the entire equation by 4 to eliminate the fractions:

4 * [(5x/4) - 9] = 4 * (x/2) 5x - 36 = 2x

Subtracting 2x from both sides:

5x - 2x - 36 = 0 3x - 36 = 0 3x = 36 x = 12

Therefore, the length of the section AB is 12 km.

Answer

The length of the section AB is 12 km (Option C).