Question

Путешественник добирался из города А в город В на машине со средней скоростью 60 км/ч, а обратно ехал на поезде со средней скоростью 90 км/ч. Какова средняя скорость его передвижения на всём пути?

Answer 1

Средняя скорость находится делением ВСЕГО расстояния на ВСЕ время, затраченное на его преодоление.
V cр=S:(t₁+t₂)
Пусть расстояние между А и В = х км 
Время в пути найдем из формулы расстояния

t =S:v

t₁=х:60
На поезде ехал t₂ часов
t₂=х:90
всего он затратил на дорогу
t₁+ t₂=
х:60+х:90=3/180+2/180=5х/180  часов
Весь путь, как мы условились,х.

Проехал путешественник его два раза, поэтому расстояние равно 2х
Средняя скорость - это расстояние, деленное на время
V ср=2х:5х/180=72 км/ч

Answer 2

Calculation of Average Speed

To calculate the average speed of the traveler on the entire journey, we need to consider the distances traveled and the time taken for each leg of the journey.

Let's assume the distance between city A and city B is D kilometers.

The traveler's speed while driving from city A to city B is 60 km/h, and the speed while returning by train is 90 km/h.

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

Average Speed = Total Distance / Total Time

The total distance traveled is 2D kilometers (going from city A to city B and returning from city B to city A).

Now, let's calculate the total time taken for the journey.

The time taken while driving from city A to city B can be calculated using the formula:

Time = Distance / Speed

The time taken while returning by train can also be calculated using the same formula.

Let's calculate the time taken for each leg of the journey:

Time taken while driving from city A to city B: D / 60 hours

Time taken while returning by train from city B to city A: D / 90 hours

The total time taken for the journey is the sum of the time taken for each leg:

Total Time = (D / 60) + (D / 90) hours

Now, we can calculate the average speed:

Average Speed = (2D) / [(D / 60) + (D / 90)] km/h

Simplifying the equation:

Average Speed = (2D) / [(3D + 2D) / 180] km/h

Average Speed = (2D) * (180 / 5D) km/h

Average Speed = 36 km/h

Therefore, the average speed of the traveler on the entire journey is 36 km/h.

Please note that this calculation assumes a constant speed throughout the journey and does not take into account factors such as traffic, stops, or delays.