Question

2 авто виїхали одночасно назустріч один одному з двох міст, відстань між якими = 960км. Через 6.5 год після початку руху вони ще не зустрілися і відстань між ними стала 115км. Знайдіть швидкість кожного авто, якщо швидкість одного із них на 10 км/год більша за другого.

Answer 1

х - скорость первого авто, х + 10 - скорость второго авто, v = х + (х + 10) = 2х + 10 км/ч -  скорость сближения, S = 960 - 115 = 845 км,  t = 6,5 ч

S = v * t

845 = (2х + 10) * 6,5

845 = 13х + 65

13х = 845 - 65

13х = 780

х = 780 : 13

х = 60 (км/ч) - скорость первого авто

60 + 10 = 70 (км/ч) - скорость второго авто

Проверка: 60 * 6,5 + 70 * 6,5 = 960 - 115

                  390 + 455 = 845

                            845 = 845 

Ответ: скорость первого авто 60 км/ч, скорость второго авто 70 км/ч.

Answer 2

Problem Analysis

We are given that two cars start simultaneously from two different cities and are moving towards each other. The distance between the cities is 960 km. After 6.5 hours, they have not yet met, and the distance between them is 115 km. We need to find the speed of each car, given that one car is traveling 10 km/h faster than the other.

Solution

Let's assume the speed of the slower car is x km/h. Since the other car is traveling 10 km/h faster, its speed will be (x + 10) km/h.

We can use the formula distance = speed × time to solve this problem.

The distance covered by the slower car in 6.5 hours is x × 6.5 km. The distance covered by the faster car in 6.5 hours is (x + 10) × 6.5 km.

According to the problem, the total distance between the two cars after 6.5 hours is 115 km. So, we can write the equation:

(x × 6.5) + ((x + 10) × 6.5) = 115

Simplifying the equation:

6.5x + 6.5(x + 10) = 115

Solving for x:

6.5x + 6.5x + 65 = 115

13x = 115 - 65

13x = 50

x = 50 / 13

x ≈ 3.846 km/h

So, the speed of the slower car is approximately 3.846 km/h.

The speed of the faster car is x + 10 km/h, which is approximately 3.846 + 10 ≈ 13.846 km/h.

Therefore, the speed of each car is approximately 3.846 km/h and 13.846 km/h.

Answer

The speed of the slower car is approximately 3.846 km/h, and the speed of the faster car is approximately 13.846 km/h.