Question

Путь от а до б автомобиль проезжает с определенной скоростью за 2,5 ч. если он увеличит скорость на 20км/ч то за 2 ч проедет путь на 15 км больше чем расстояние от а до б. Найдите расстояние от А до Б

Answer 1

Пусть х (км/ч) - скорость автомобиля.
2,5х + 15 = 2 * (х + 20)
2,5х + 15 = 2х + 40
2,5х - 2х = 40 - 15
0,5х = 25
х = 25 : 0,5
х = 50 (км/ч) - скорость автомобиля
2,5 * 50 = 125 (км) - расстояние между пунктами
Ответ: 125 км. 

Answer 2

Problem Analysis

We are given that a car travels from point A to point B at a certain speed for 2.5 hours. If the car increases its speed by 20 km/h, it can cover a distance that is 15 km longer than the distance from A to B in 2 hours. We need to find the distance from point A to point B.

Solution

Let's assume the initial speed of the car is v km/h and the distance from A to B is d km.

According to the given information, we can set up the following equations:

Equation 1: The car travels at a certain speed for 2.5 hours to cover the distance from A to B. d = v * 2.5 Equation 2: If the car increases its speed by 20 km/h, it can cover a distance that is 15 km longer than the distance from A to B in 2 hours. (d + 15) = (v + 20) * 2 To solve this system of equations, we can substitute Equation 1 into Equation 2:

(v * 2.5 + 15) = (v + 20) * 2

Now, let's solve this equation to find the value of v.

Calculation

Expanding the equation:

2.5v + 15 = 2v + 40

Simplifying the equation:

0.5v = 25

Dividing both sides by 0.5:

v = 50

Now that we have the value of v, we can substitute it back into Equation 1 to find the distance d:

d = 50 * 2.5 = 125

Therefore, the distance from point A to point B is 125 km.

Answer

The distance from point A to point B is 125 km.

Explanation

The car initially travels at a speed of 50 km/h for 2.5 hours, covering a distance of 125 km. If the car increases its speed by 20 km/h, it can cover a distance that is 15 km longer than the distance from A to B in 2 hours. By solving the equations, we find that the distance from point A to point B is indeed 125 km.