Question

ПОМОГИТЕ ПРОШУ . Из двух городов одновременно навстречу друг другу выехали автомобиль и автобус. Автомобиль до встречи проехал 270, а автобус — 180 км. Найдите скорость автомобиля, если она на – 30 км/ч больше скорости автобуса. ​

Answer 1

Пусть искомая скорость автомобиля = V

Тогда по условию скорость автобуса =V-30

Время, которое потратит автобус на путь до встречи с автомобилем будет определяться

частному пройденного пути и скорости автобуса:

$t _{автобус}= \frac{180}{v - 30}$

Для автомобиля же это время будет

$t_{автомобиль} = \frac{270}{v}$

Так как до встречи автомобиль и автобус проехали одинаковое время, то

$t_{автобус}=t_{автомобиль}$

поэтому:

$\frac{180}{v - 30} = \frac{270}{v}$

решаем:

$\frac{2 \times 90}{v - 30} = \frac{3 \times 90}{v} \\ \frac{2}{v - 30} = \frac{3}{v} \\ 2v = 3v - 90 \\ v = 90$

Ответ: Скорость автомобиля =90 км/ч

Answer 2

Problem Analysis

We are given that a car and a bus start from two different cities and travel towards each other. The car travels a distance of 270 km, while the bus travels a distance of 180 km. We need to find the speed of the car, given that it is 30 km/h faster than the speed of the bus.

Solution

Let's assume the speed of the bus is x km/h. According to the given information, the speed of the car is x + 30 km/h.

We can use the formula speed = distance / time to find the time taken by each vehicle to travel their respective distances.

For the car: Speed of car = (Distance traveled by car) / (Time taken by car)

For the bus: Speed of bus = (Distance traveled by bus) / (Time taken by bus)

Since the car and the bus start at the same time and meet each other, the time taken by both vehicles will be the same.

Let's calculate the time taken by each vehicle:

For the car: Time taken by car = (Distance traveled by car) / (Speed of car) = 270 / (x + 30)

For the bus: Time taken by bus = (Distance traveled by bus) / (Speed of bus) = 180 / x

Since the time taken by both vehicles is the same, we can equate the two expressions:

270 / (x + 30) = 180 / x

To solve this equation, we can cross-multiply and solve for x:

270x = 180(x + 30)

Simplifying the equation:

270x = 180x + 5400

90x = 5400

x = 60

Therefore, the speed of the bus is 60 km/h. Since the speed of the car is 30 km/h faster, the speed of the car is:

Speed of car = 60 + 30 = 90 km/h

So, the speed of the car is 90 km/h.

Answer

The speed of the car is 90 km/h.