Question

Города А, В, С вместе с соединяющими их прямыми дорогами образуют треугольник. Известно, что прямой путь из А в Б на 200 км короче объезда через С, а прямой путь из А в С на 300 км короче объезда через В. Найдите расстояние между городами В и С

Answer 1

Запишем все в виде уравнений
AC+BC-200=AB
AB+BC-300=AC
подствавим во второе уравнение первое

AC+BC-200+BC-300=AC

2BC=500
BC=250км

Answer 2

Problem Analysis

We are given three cities, A, B, and C, along with the direct roads connecting them. We are also given that the direct path from A to B is 200 km shorter than going through C, and the direct path from A to C is 300 km shorter than going through B. We need to find the distance between cities B and C.

Solution

Let's assume the distance between A and B is x km, the distance between A and C is y km, and the distance between B and C is z km.

According to the given information, the direct path from A to B is 200 km shorter than going through C. This can be expressed as: x = y + 200

Similarly, the direct path from A to C is 300 km shorter than going through B. This can be expressed as: y = z + 300

We need to find the distance between cities B and C, which is z.

To solve this system of equations, we can substitute the value of y from the second equation into the first equation: x = (z + 300) + 200 x = z + 500

Now, we have two equations: x = z + 500 y = z + 300

To find the distance between cities B and C, we need to solve for z. We can subtract the second equation from the first equation: x - y = (z + 500) - (z + 300) x - y = z + 500 - z - 300 x - y = 200

Therefore, the distance between cities B and C is 200 km.

Answer

The distance between cities B and C is 200 km.