Question

Путь из города в село турист прошёл со скоростью 4,8 км/ч. На обратном пути он увеличил скорость до 6 км/ч, что позволило ему пройти это расстояние на 1 быстрее. Найдите расстояние от города до села. Решите с помощью уравнения.

Answer 1

Путь из города в село:
V₁ = 4.8  км/ч   скорость
t₁ = t   часов    время в пути
S =  4.8t  км     расстояние

Путь из села в город (обратный путь):
V₂ = 6 км/ч
t₂ = (t +1) часов
S₂ = 6(t - 1)  км

S₂ = S₁  ⇒  уравнение:
6(t-1) = 4.8t
6t  - 6  = 4.8t
6t - 4.8t = 6
1.2t = 6
t=6/1.2
t=5 (часов) время на путь из  города в село
S₁=5*4.8 = 24 (км) расстояние от города до села
(или S₂ = 6*(5-1) = 6*4  = 24 (км)  )

Ответ:  24 км расстояние от города до села.

Answer 2

Problem Analysis

We are given that a tourist walked from a city to a village at a speed of 4.8 km/h. On the return journey, the tourist increased their speed to 6 km/h and completed the distance 1 hour faster. We need to find the distance from the city to the village.

Solution

Let's assume the distance from the city to the village is d km.

On the forward journey, the tourist traveled at a speed of 4.8 km/h. Therefore, the time taken for the forward journey can be calculated using the formula:

Time taken for forward journey = Distance / Speed = d / 4.8

On the return journey, the tourist increased their speed to 6 km/h. Therefore, the time taken for the return journey can be calculated using the formula:

Time taken for return journey = Distance / Speed = d / 6

According to the problem, the return journey was completed 1 hour faster than the forward journey. So we can write the equation:

Time taken for forward journey - Time taken for return journey = 1

Substituting the values, we get:

d / 4.8 - d / 6 = 1

To solve this equation, we can multiply through by the least common multiple (LCM) of the denominators, which is 28. This gives us:

28 * (d / 4.8) - 28 * (d / 6) = 28

Simplifying further:

7d - 9.333d = 28

-2.333d = 28

Dividing both sides by -2.333, we get:

d = -28 / 2.333

Therefore, the distance from the city to the village is approximately 12 km.

Answer

The distance from the city to the village is approximately 12 km.