Question

Из города А в город В, расстояние между которыми 200 км, выехал автобус. Через 1 ч 20 мин вслед за ним выехал автомобиль, скорость которого в 1,5 раза больше скорости автобуса. Найдите скорость автобуса, если в город В они прибыли одновременно.

Answer 1

Х км/ч скорость автобуса
1,5х скорость автомобиля
200/х ч времени был в пути автобус
200/1,5х ч времени был в пути автомобиль
По условию известно, что автомобиль выехал через 1ч20мин = 1 20/60 = 4/3 ч после автобуса и прибыл в город В одновременно с ним
.200/х - 200/1,5х = 4/3 (умножим обе части на 3х)
600 - 400 = 4х
4х = 200
х = 50
Ответ. 50 км/ч скорость автобуса.

Answer 2

Problem Analysis

We are given that a bus and a car travel from City A to City B, a distance of 200 km. The car starts 1 hour and 20 minutes after the bus and has a speed 1.5 times greater than the speed of the bus. We need to find the speed of the bus if they both arrive in City B at the same time.

Solution

Let's assume the speed of the bus is x km/h. Since the car's speed is 1.5 times greater than the speed of the bus, the speed of the car is 1.5x km/h.

We can use the formula distance = speed × time to calculate the time taken by each vehicle to travel from City A to City B.

For the bus: - Distance = 200 km - Speed = x km/h - Time = 200/x hours

For the car: - Distance = 200 km - Speed = 1.5x km/h - Time = 200/(1.5x) hours

According to the problem, the car starts 1 hour and 20 minutes (1.33 hours) after the bus. So, the time taken by the car is 1.33 hours less than the time taken by the bus.

Equating the times taken by the bus and the car, we have the equation:

200/x = 200/(1.5x) + 1.33

To solve this equation, we can multiply both sides by x to eliminate the denominators:

200 = 200/1.5 + 1.33x

Simplifying further:

200 = 133.33 + 1.33x

Subtracting 133.33 from both sides:

66.67 = 1.33x

Dividing both sides by 1.33:

x = 50

Therefore, the speed of the bus is 50 km/h.

Answer

The speed of the bus is 50 km/h.