Question

Из посёлка выехал автобус, а через час выехал автомобиль и догнал автобус через 1,5 ч. На каком расстоянии от посёлка автомобиль догнал автобус, если скорость автомобиля на 40 км/ч больше скорости автобуса (автобус в пути не делал остановок)?

Answer 1

Пусть х (км/ч) - скорость автобуса, тогда х + 40 (км/ч) - скорость автомобиля. Уравнение:
2,5х = 1,5 * (х + 40)
2,5х = 1,5х + 60
2,5х - 1,5х = 60
х = 60 (км/ч) - скорость автобуса
60 + 40 = 100 (км/ч) - скорость автомобиля
2,5 * 60 = 1,5 * 100 = 150 (км) - на таком расстоянии от посёлка автомобиль догнал автобус.
Ответ: 150 км.

Answer 2

Problem Analysis

We are given that a bus left a village, and an hour later, a car left and caught up with the bus after 1.5 hours. The car's speed is 40 km/h faster than the bus's speed. We need to determine the distance from the village where the car caught up with the bus.

Solution

Let's assume the speed of the bus is x km/h. Since the car's speed is 40 km/h faster, the car's speed is x + 40 km/h.

We know that the car caught up with the bus after 1.5 hours. During this time, the bus traveled for 1 hour longer than the car. Therefore, the distance traveled by the bus is x * (1 + 1.5) km, and the distance traveled by the car is (x + 40) * 1.5 km.

Since the car caught up with the bus, the distances traveled by both vehicles must be equal. Therefore, we can set up the following equation:

x * (1 + 1.5) = (x + 40) * 1.5

Now, let's solve this equation to find the value of x.

Calculation

x * (1 + 1.5) = (x + 40) * 1.5

Simplifying the equation:

2.5x = 1.5x + 60

Subtracting 1.5x from both sides:

2.5x - 1.5x = 60

Simplifying further:

x = 60

Therefore, the speed of the bus is 60 km/h.

Now, let's calculate the distance from the village where the car caught up with the bus.

The distance traveled by the bus is 60 * (1 + 1.5) = 180 km.

Therefore, the car caught up with the bus at a distance of 180 km from the village.

Answer

The car caught up with the bus at a distance of 180 km from the village.

Explanation

The bus traveled for 2.5 hours at a speed of 60 km/h, covering a distance of 150 km. The car traveled for 1.5 hours at a speed of 100 km/h, covering a distance of 150 km. Since the car's speed is 40 km/h faster than the bus's speed, it caught up with the bus after 1.5 hours.