Question

На первой половине пути автобус двигался со скоростью в 8 раз больше чем на второй.Средняя скорость на всем пути 16 км\ч.Определите скорость автобуса на каждом участке пути? Помогите плиз)

Answer 1

Пусть скорость автобуса на второй половине пути равна v, а весь путь равен 2S. 

Тогда время передвижения по второй половине пути t2=S/v. Время передвижения по первой половине пути t1=S/(8v). Средняя скорость vср = 2S / (S/v + S/(8v)) = 16v/9. Отсюда v=9vср/16. 

Подставляем vср=16 км/ч и получаем, что скорость на второй половине пути 9 км/ч, а на первой 72 км/ч.

Answer 2

Problem Analysis

We are given that a bus traveled at a speed 8 times faster on the first half of the journey compared to the second half. The average speed for the entire journey is 16 km/h. We need to determine the speed of the bus on each segment of the journey.

Solution

Let's assume the speed of the bus on the second half of the journey is x km/h. According to the given information, the speed on the first half of the journey is 8 times faster, so the speed on the first half is 8x km/h.

To find the average speed, we can use the formula:

Average Speed = Total Distance / Total Time

Since the distance traveled on both halves of the journey is the same, we can simplify the formula to:

Average Speed = 2 * Distance / Total Time

We know that the average speed is 16 km/h, so we can write the equation as:

16 = 2 * Distance / Total Time

To find the speed on each segment, we need to calculate the total time and distance for the entire journey.

Let's assume the distance traveled on each half of the journey is d km. Therefore, the total distance for the entire journey is 2d km.

The time taken to travel the first half of the journey is d / (8x) hours, and the time taken to travel the second half is d / x hours. Therefore, the total time for the entire journey is d / (8x) + d / x hours.

Substituting these values into the equation, we get:

16 = 2 * 2d / (d / (8x) + d / x)

Simplifying the equation, we get:

16 = 4x / (1/8 + 1)

Solving for x, we find:

x = 16 / (4/9) = 36 km/h

Therefore, the speed of the bus on the second half of the journey is 36 km/h, and the speed on the first half is 8x = 8 * 36 = 288 km/h.

Answer

The speed of the bus on the first half of the journey is 288 km/h, and the speed on the second half is 36 km/h.