Question

Из лагеря на станцию, расстояние между которыми 20 км, вышел турист. Если турист увеличит свою скорость в два раза и уменьшит на 3 км/час, то за 4 часа он пройдет больше 20 км. Если он уменьшит скорость на 1 км/час, то за 5 часов он не дойдет до станции. Оцени скорость туриста. x – скорость туриста.ПОМОГИТЕ!​

Answer 1

Ответ:

4,5 км/час - скорость туриста

Пошаговое объяснение:

х км/час скорость туриста

2х - 3 км/час - турист увеличит свою скорость в два раза и уменьшит на 3 км/час

х - 1  км/час - турист уменьшит скорость на 1 км/час

4(2х-3) > 20  8х - 12 > 20    8х > 32    х > 32/8   х > 4 км/час

5(х-1) < 20     5х - 5 < 20     5х < 25    х  < 25/5   х < 5 км/час

Получается, что 5 > х > 4, значит х = 4,5 км/час - скорость туриста

4(2х-3) > 20  4(2*4,5 - 3) = 4*6 = 24 км пройдёт турист за 4 часа

5(х-1) < 20     5(4,5 - 1) = 5*3,5 = 17,5 км пройдёт турист за 5 часов

Answer 2

Problem Analysis

We are given that a tourist walked from a camp to a train station, which are 20 km apart. We are also given two conditions: 1. If the tourist doubles their speed and reduces it by 3 km/h, they will cover more than 20 km in 4 hours. 2. If the tourist reduces their speed by 1 km/h, they will not reach the station in 5 hours.

We need to determine the speed of the tourist.

Solution

Let's assume the speed of the tourist is x km/h.

According to the first condition, if the tourist doubles their speed and reduces it by 3 km/h, they will cover more than 20 km in 4 hours. Mathematically, this can be represented as:

Distance = Speed × Time

For the first condition: - Distance = More than 20 km - Speed = 2x - 3 km/h - Time = 4 hours

Using the formula, we can write the equation as:

(2x - 3) × 4 > 20

Simplifying the equation, we get:

8x - 12 > 20

Adding 12 to both sides, we get:

8x > 32

Dividing both sides by 8, we get:

x > 4

So, the speed of the tourist is greater than 4 km/h.

According to the second condition, if the tourist reduces their speed by 1 km/h, they will not reach the station in 5 hours. Mathematically, this can be represented as:

Distance = Speed × Time

For the second condition: - Distance = Less than or equal to 20 km - Speed = x - 1 km/h - Time = 5 hours

Using the formula, we can write the equation as:

(x - 1) × 5 ≤ 20

Simplifying the equation, we get:

5x - 5 ≤ 20

Adding 5 to both sides, we get:

5x ≤ 25

Dividing both sides by 5, we get:

x ≤ 5

So, the speed of the tourist is less than or equal to 5 km/h.

Combining the two conditions, we can conclude that the speed of the tourist is greater than 4 km/h and less than or equal to 5 km/h.

Therefore, the estimated speed of the tourist is between 4 km/h and 5 km/h.

Please note that the exact speed of the tourist cannot be determined without additional information.

Answer

The estimated speed of the tourist is between 4 km/h and 5 km/h.