Question

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

Answer 1

Х скорость первого автомобиля
0,7х скорость второго автомобиля

х-0,7х=30
0,3=30
х=100 км/ч скорость 1 автомобиля
100*0,7=70 км /ч скорость 2 автомобиля
100+70=170 км/ч скорость сближения
510:170=через 3 часа встретятся

Answer 2

Problem Analysis

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

Solution

Let's denote the speed of the first car as v1 and the speed of the second car as v2. We are given that v1 = 0.7 * v2 and v2 = v1 + 30.

To find the time it takes for the cars to meet, we can use the formula time = distance / relative speed. The relative speed is the sum of the speeds of the two cars.

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

1. Calculate the speed of the first car: - v1 = 0.7 * v2.

2. Calculate the speed of the second car: - v2 = v1 + 30.

3. Calculate the relative speed: - relative speed = v1 + v2.

4. Calculate the time it takes for the cars to meet: - time = distance / relative speed.

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

Calculation

1. Calculate the speed of the first car: - v1 = 0.7 * v2. - v1 = 0.7 * (v1 + 30). - v1 = 0.7v1 + 21. - 0.3v1 = 21. - v1 = 21 / 0.3. - v1 = 70 km/h.

2. Calculate the speed of the second car: - v2 = v1 + 30. - v2 = 70 + 30. - v2 = 100 km/h.

3. Calculate the relative speed: - relative speed = v1 + v2. - relative speed = 70 + 100. - relative speed = 170 km/h.

4. Calculate the time it takes for the cars to meet: - time = distance / relative speed. - time = 510 / 170. - time = 3 hours.

Answer

The cars will meet after 3 hours.

Please let me know if I can help you with anything else.