Question

Автобус и грузовая машина, скорость которой на 20 км/ч больше скорости автобуса, выехали одновременно навстречу друг другу из двух городов, расстояние между которыми 576 км. Определи скорости автобуса и грузовой машины, если известно, что они встретились через 4 ч. после выезда.

Answer 1

576:4=144 (км/ч) скорость сближения или сумма скоростей
х - скорость автобуса
х+20 - скорость грузовика
х+(х+20)=144
2х+20=144
2х=144-20
2х=124
х=124:2
х=62 (км/ч) автобус
62+20=82 (км/ч) грузовик
Ответ: скорость автобуса 62 км/ч, а грузовика 82 км/ч

Answer 2

Problem Analysis

We are given that a bus and a truck, whose speed is 20 km/h greater than the speed of the bus, start from two cities and travel towards each other. The distance between the cities is 576 km. They meet after 4 hours. We need to determine the speeds of the bus and the truck.

Solution

Let's assume the speed of the bus is x km/h. Since the speed of the truck is 20 km/h greater than the speed of the bus, the speed of the truck is (x + 20) km/h.

We know that the distance traveled by an object is equal to its speed multiplied by the time taken. In this case, the bus and the truck meet after 4 hours, so the distance traveled by the bus is 4x km and the distance traveled by the truck is 4(x + 20) km.

Since they meet, the sum of the distances traveled by the bus and the truck must be equal to the total distance between the cities, which is 576 km. Therefore, we can write the equation:

4x + 4(x + 20) = 576

Simplifying the equation:

4x + 4x + 80 = 576

8x + 80 = 576

8x = 496

x = 62

The speed of the bus is 62 km/h. Since the speed of the truck is 20 km/h greater, the speed of the truck is (62 + 20) = 82 km/h.

Therefore, the speed of the bus is 62 km/h and the speed of the truck is 82 km/h.

Answer

The speed of the bus is 62 km/h and the speed of the truck is 82 km/h.