Question

Два автомобиля одновременно выехали навстречу друг другу из городов, находящихся на расстоянии 510 км. Скорость первого автомобиля составляет 70% скорости второго. Через сколько часов автомобили встретятся, если скорость второго больше скорости первого на 30 км/ч?

Answer 1

Х скорость первого
0,7х скорость второго
х-0,7х=30
0,3х=30
х=100 км/ч скорость первого
100*0,7=70 км/ч скорость второго
100+70=170 км/ч скорость сближения
510:170= через 3 часа автомобили встретятся

Answer 2

Problem Analysis

We are given that two cars start simultaneously from two cities that are 510 km apart. The speed of the first car is 70% of the speed of the second car, and the second car is 30 km/h faster than the first car. We need to determine how many hours it will take for the cars to meet.

Solution

Let's assume the speed of the first car is x km/h. Then the speed of the second car will be x + 30 km/h.

We can use the formula distance = speed × time to calculate the time it takes for the cars to meet.

The distance traveled by the first car is x × t (where t is the time in hours), and the distance traveled by the second car is (x + 30) × t.

Since the total distance traveled by both cars is 510 km, we can write the equation:

x × t + (x + 30) × t = 510

Simplifying the equation:

2x × t + 30 × t = 510

Factoring out t:

t(2x + 30) = 510

Dividing both sides by 2x + 30:

t = 510 / (2x + 30)

Now we can substitute the value of x (the speed of the first car) into the equation and solve for t.

Calculation

Let's calculate the time it takes for the cars to meet.

Given that the speed of the first car is