Question

Автобус и грузовая машина, скорость которой на 19 км/ч больше скорости автобуса, выехали одновременно навстречу друг другу из двух городов, расстояние между которыми 429 км. Найди скорости автобуса и грузовой машины, если известно, что они встретились через 3 ч. после выезда.

Answer 1

Пускай скорость автобуса - х км/час, тогда скорость грузовой - х+19 км/час. Так как они едут навстречу друг другу, то скорость сближения = х+х+19 = 2х+19 км/час
Составляем уравнение:
скорость*время=расстояние
(2х+19)*3=429
6х+57=429
6х=372
х=62 (км/час) - скорость автобуса
Тогда скорость грузовой машины = 81 (км/час)
Ответ: 62 км/час, 81 км/час

Answer 2

Problem Analysis

We are given that a bus and a truck, with a speed 19 km/h greater than the bus, start from two cities that are 429 km apart. We need to find the speeds of the bus and the truck, given that they meet each other 3 hours after starting.

Solution

Let's assume the speed of the bus is x km/h. Since the speed of the truck is 19 km/h greater than the bus, the speed of the truck is x + 19 km/h.

We know that the time taken by both vehicles to meet each other is 3 hours.

To find the speeds of the bus and the truck, we can use the formula: speed = distance / time.

The distance traveled by the bus in 3 hours is 3x km, and the distance traveled by the truck in 3 hours is 3(x + 19) km.

Since the total distance between the two cities is 429 km, the sum of the distances traveled by the bus and the truck should be equal to 429 km.

Therefore, we can set up the following equation:

3x + 3(x + 19) = 429

Simplifying the equation:

3x + 3x + 57 = 429

6x + 57 = 429

6x = 429 - 57

6x = 372

x = 372 / 6

x = 62

So, the speed of the bus is 62 km/h.

The speed of the truck is 19 km/h greater than the bus, so the speed of the truck is 62 + 19 = 81 km/h.

Therefore, the speed of the bus is 62 km/h and the speed of the truck is 81 km/h.

Answer

The speed of the bus is 62 km/h and the speed of the truck is 81 km/h.