Question

Два автомобиля выехали одновременно навстречу друг другу из двух городов, расстояние между которыми равно 960 км. Через 6,5 ч после начала движения они ещё не встретились и расстояние между ними было 115 км. Найдите скорость каждого автомобиля, если скорость одного из них больше на 10 км/ч скорости второго

Answer 1

960-115=845км проехали автомобили за 6,5часов
845:6,5=130км/час скорость сближения (сумма скоростей)
х скорость одного автомобиля
х-10 второго
х+(х-10)=130
2х=140
х=70км/час скорость первого
70-10=60км/час второго

Answer 2

Problem Analysis

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 of driving, 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. Then the speed of the faster car will be (x + 10) km/h.

We can use the formula distance = speed × time to calculate the distance traveled by each car.

For the slower car: - Distance traveled = speed × time = x km/h × 6.5 h = 6.5x km

For the faster car: - Distance traveled = speed × time = (x + 10) km/h × 6.5 h = 6.5x + 65 km

Since the total distance between the two cars is 960 km, we can set up the equation:

Distance traveled by the slower car + Distance traveled by the faster car = Total distance 6.5x + 6.5x + 65 = 960

Simplifying the equation: 13x + 65 = 960 13x = 895 x = 895 / 13 x ≈ 68.85

Therefore, the speed of the slower car is approximately 68.85 km/h, and the speed of the faster car is approximately 78.85 km/h.

Answer

The speed of the slower car is approximately 68.85 km/h, and the speed of the faster car is approximately 78.85 km/h.