Question

Участок прямолинейного шоссе между городами А и В наиболее подвержен дорожно - транспортным происшествием. В пункте О это го участка произошла ав а рия. Пункт скорой помощи находится на середине участка АВ , в пункте М , рассто я ние от которого до пункта О равно 3 км. Расстояние от пункта О до одного из концов участка АВ равно 1/5 длины этого участка. Определите расстояние между пунктами А и В .

Answer 1

Расстояние АО = 1/5 * АВ = 0,2*АВ;  Расстояние AМ = 1/2 * AB = 0,5*AB
ОМ = АМ - АО = 0,5*АВ - 0,2*АВ = 0,3*АВ
ОМ = 3 км
0,3*АВ = 3
АВ = 10 км
Ответ: расстояние между пунктами А и В 10 км.

Answer 2

Problem Analysis

We are given a straight highway segment between cities A and B, and there was an accident at point O on this segment. The distance from point O to the nearest emergency medical service (EMS) station, located at point M, is 3 km. The distance from point O to one of the ends of the highway segment AB is 1/5 of the length of the segment AB. We need to determine the distance between points A and B.

Solution

To solve this problem, let's assign variables to the unknown distances: - Distance from point A to point O: x km - Distance from point O to point B: 4x km (since the distance from O to one end of AB is 1/5 of the length of AB, the distance from O to the other end is 4/5 of the length of AB)

Now, let's set up an equation using the given information: - Distance from point A to point O + Distance from point O to point B = Length of highway segment AB - x + 4x = Length of AB

We also know that the distance from point O to point M is 3 km. Since point M is located in the middle of AB, the distance from A to M is half the length of AB. Therefore, we can write another equation: - Distance from point A to point M = 1/2 * Length of AB - x + 3 = 1/2 * Length of AB

Now, we have a system of two equations with two unknowns. We can solve this system to find the values of x and the Length of AB.

Solving the System of Equations

Let's solve the system of equations using substitution:

From the equation x + 4x = Length of AB, we can simplify it to 5x = Length of AB.

Substituting this value into the equation x + 3 = 1/2 * Length of AB, we get: x + 3 = 1/2 * 5x x + 3 = 5/2 * x 2x + 6 = 5x 6 = 5x - 2x 6 = 3x x = 2

Now, we can substitute the value of x back into the equation Length of AB = 5x to find the length of AB: Length of AB = 5 * 2 = 10 km

Therefore, the distance between points A and B is 10 km.

Conclusion

The distance between points A and B on the straight highway segment is 10 km. This was determined by setting up a system of equations using the given information and solving for the unknown distances. The distance from point O to the nearest EMS station, located at point M, is 3 km.