Question

По шоссе идут две машины с одной и той же скростью.Если первая увеличит скорось на 10км\ч , а вторая уменьшит скорость на 10 км\ч,то перваяза 2 часа пройдет столько же, сколько вторая за 3 часа.С какой скоростью идут автомашины?

Answer 1

Пусть первоначальная скорость каждой из машин V км/ч.
После изменений   скорость I машины станет V₁= (V+10) км/ч , а
II машины V₂= (V-10) км/ч.
Тогда  расстояние, которое пройдет I машина за  2 часа  пути
будет  S₁= 2*(V+10) км.  
А расстояние, которое пройдет II машина за 3 часа,  S₂= 3*(V-10)  км .
Зная, что S₁=S₂  составим уравнение:
2*(V+10) = 3*(V-10)
2V +20 = 3V - 30
2V  - 3V =  -30 - 20
-V= -50
V=50  (км/ч)  первоначальная скорость машин

Ответ: 50 км/ч.

Answer 2

Problem Analysis

We are given that two cars are traveling on a highway at the same speed. If the first car increases its speed by 10 km/h and the second car decreases its speed by 10 km/h, the first car will cover the same distance in 2 hours as the second car covers in 3 hours. We need to find the speed at which the cars are traveling.

Solution

Let's assume the initial speed of both cars is x km/h.

According to the given information, if the first car increases its speed by 10 km/h, its new speed will be (x + 10) km/h. Similarly, if the second car decreases its speed by 10 km/h, its new speed will be (x - 10) km/h.

We are also given that the first car covers the same distance in 2 hours as the second car covers in 3 hours. Let's calculate the distances covered by each car.

The distance covered by the first car in 2 hours is given by: Distance1 = Speed1 × Time1 = (x + 10) × 2 km

The distance covered by the second car in 3 hours is given by: Distance2 = Speed2 × Time2 = (x - 10) × 3 km

According to the problem, these distances are equal: (x + 10) × 2 = (x - 10) × 3

Let's solve this equation to find the value of x, which represents the initial speed of the cars.

Expanding the equation, we get: 2x + 20 = 3x - 30

Simplifying the equation, we get: 20 + 30 = 3x - 2x 50 = x

Therefore, the initial speed of the cars is 50 km/h.

Answer

The cars are traveling at a speed of 50 km/h.