Question

!СРОЧНО! Со Львова в Киев одновременно выехали автобус и автомобиль.Скорость автомобиля на 30 км / ч больше скорости автобуса, поэтому он прибыл в Киев на 3 часа раньше. Найдите скорость автобуса и автомобиля если расстояние между городами 540 км. Ответ в книге : 60 км/ч и 90 км/ч

Answer 1

Problem Analysis

We are given that a bus and a car simultaneously left Lviv for Kyiv. The car's speed is 30 km/h faster than the bus, and as a result, it arrived in Kyiv 3 hours earlier. We need to find the speeds of the bus and the car if the distance between the cities is 540 km.

Solution

Let's assume the speed of the bus is x km/h. Since the car's speed is 30 km/h faster, the speed of the car is (x + 30) km/h.

We know that the time taken by the bus to travel the distance is given by:

Time taken by the bus = Distance / Speed of the bus

Similarly, the time taken by the car to travel the distance is given by:

Time taken by the car = Distance / Speed of the car

According to the problem, the car arrived in Kyiv 3 hours earlier than the bus. So, we can write the equation:

Time taken by the bus - Time taken by the car = 3 hours

Substituting the values from the above equations, we get:

(Distance / Speed of the bus) - (Distance / Speed of the car) = 3

Substituting the value of the distance (540 km), we have:

(540 / x) - (540 / (x + 30)) = 3

To solve this equation, we can multiply through by x(x + 30) to eliminate the denominators:

540(x + 30) - 540x = 3x(x + 30)

Simplifying the equation:

540x + 16200 - 540x = 3x^2 + 90x

16200 = 3x^2 + 90x

3x^2 + 90x - 16200 = 0

Now, we can solve this quadratic equation to find the value of x, which represents the speed of the bus.

Using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

where a = 3, b = 90, and c = -16200.

Solving this equation, we get two possible values for x: -180 and 30. Since speed cannot be negative, we discard the negative value.

Therefore, the speed of the bus is 30 km/h.

Since the speed of the car is 30 km/h faster, the speed of the car is (30 + 30) km/h = 60 km/h.

So, the speed of the bus is 30 km/h, and the speed of the car is 60 km/h.

Answer

The speed of the bus is 30 km/h, and the speed of the car is 60 km/h.