Question

Если расстояние города от другого, скоростной поезд проходит за 12 ч, а пассажирский за 15 ч. Если они вышли одновременно на встречу друг другу, через какое время они встретятся?СРОЧНО!!!С ПОЛНЫМ решением)

Answer 1

Пусть расстояние между городами  равно х км, тогда скорость 1 поезда V1=х/15  км/час, а скорость 2 поезда  V2= х/12 км/час.
Cкорость сближения равна  V1+V2=x/15+x/12=9x/60=3x/20 (км/ч).
Время, через которое поезда встретятся равнo:

  $t= \frac{S}{V}=\frac{x}{V_1+V_2}= \frac{x}{ \frac{3x}{20} } = \frac{1}{3/20} = \frac{20}{3} =6\frac{2}{3}=$  часа=6ч 40 мин

$P.S.\; \; t= \frac{S}{V}= \frac{x}{\frac{x}{t_1}+\frac{x}{t_2}}=\frac{x}{\frac{xt_1+xt_2}{t_1t_2}}=\frac{x}{\frac{x(t_1+t_2)}{t_1t_2}}= \frac{t_1t_2}{t_1+t_2}$

Answer 2

Problem Analysis

We are given that a high-speed train takes 12 hours to travel a certain distance between two cities, while a passenger train takes 15 hours to cover the same distance. Both trains start at the same time and travel towards each other. We need to determine how long it will take for the two trains to meet.

Solution

To solve this problem, we can use the concept of relative speed. The relative speed between two objects moving towards each other is the sum of their individual speeds. In this case, the relative speed of the two trains is the sum of the speed of the high-speed train and the speed of the passenger train.

Let's assume the distance between the two cities is D.

The speed of the high-speed train can be calculated as D/12 (since it takes 12 hours to cover the distance D), and the speed of the passenger train can be calculated as D/15 (since it takes 15 hours to cover the distance D).

The relative speed of the two trains is (D/12) + (D/15).

To find the time it takes for the two trains to meet, we can divide the distance between the two cities by the relative speed of the trains:

Time = Distance / Relative Speed

Substituting the values, we get:

Time = D / ((D/12) + (D/15))

Simplifying the expression, we can find the value of time.

Calculation

Let's calculate the time it takes for the two trains to meet.

Time = D / ((D/12) + (D/15))

Simplifying the expression:

Time = D / ((5D + 4D) / 60)

Time = D / (9D / 60)

Time = 60 / 9

Time = 6.67 hours

Therefore, the two trains will meet after approximately 6.67 hours.

Answer

If the high-speed train takes 12 hours to cover the distance between the two cities, and the passenger train takes 15 hours to cover the same distance, and they start at the same time and travel towards each other, they will meet after approximately 6.67 hours.