Question

два пешехода вышли одновременно навстречу друг другу из пунктов А и В. Привстречи оказалось,что один из них прошёл 2\9 всего расстояния от А до В и ещё 1 1\2 км,а другой прошёл 1\3 всего расстояния от А до В и ещё 2 1\2км. Чему равно расстояние от пункта А до пункта В?

Answer 1

Пусть х все расстояние.

Первый прошел 2/9х+1,5

Второй прошел 1/3х+2,5

Составим уравнение:

2/9х+1,5+1/3х+2,5=х

х=9 км.

Проверим: 9*2/9+1,5=3,5 км. 9*1,3+2,5=5,5 км. Всего 9 км.

Answer 2

Problem Analysis

We have two pedestrians who start walking towards each other from points A and B. When they meet, one of them has covered 2/9 of the total distance from A to B and an additional 1 1/2 km, while the other has covered 1/3 of the total distance from A to B and an additional 2 1/2 km. We need to find the distance from point A to point B.

Solution

Let's assume the total distance from point A to point B is D km.

According to the problem, one pedestrian has covered 2/9 of the total distance and an additional 1 1/2 km. This can be expressed as:

(2/9)D + 1 1/2 = (19/9)D/2 + 3/2 = (19D + 27)/18

Similarly, the other pedestrian has covered 1/3 of the total distance and an additional 2 1/2 km. This can be expressed as:

(1/3)D + 2 1/2 = (7/3)D/2 + 5/2 = (7D + 15)/6

Since they meet at the same point, the distances covered by both pedestrians should be equal. Therefore, we can equate the two expressions:

(19D + 27)/18 = (7D + 15)/6

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

6(19D + 27) = 18(7D + 15) 114D + 162 = 126D + 270 12D = 108 D = 9

Therefore, the distance from point A to point B is 9 km.

Answer

The distance from point A to point B is 9 km.