Question

Плииииииииз))) Из пункта А в пункт Б вышел пассажирский поезд. Через три часа вслед за ним вышел скорый поезд. Скорый поезд догнал пассажирский в середине пути из А в Б. в момент прибытия скорого поезда в Б пассажирский поезд прошел 13/16 всего пути. Сколько времени требуется скорому поезду на прохождение всего пути от А до Б

Answer 1

1-весь путь
х-скорость пасс.
у-скорость скорого.
Система уравнений
$\frac{0,5}{x} = \frac{0.5}{y} +3 \\ \frac{13/16}{x} = \frac{1}{y} +3 \\ \\ x= \frac{0,5}{ \frac{0.5}{y} +3} \\ x=\frac{13/16}{\frac{1}{y}+3} \\ \\ \frac{0,5}{ \frac{0.5}{y} +3}=\frac{13/16}{\frac{1}{y}+3} \\ \\ 0,5(\frac{1}{y}+3)=13/16(\frac{0.5}{y} +3)$  умножим на 16
$8(\frac{1}{y}+3)=13(\frac{0.5}{y} +3) \\ \frac{8}{y}+24=\frac{6.5}{y} +39 \\ \frac{8}{y}-\frac{6.5}{y} =39-24 \\ \frac{1,5}{y} =15 \\ y=1.5/15 \\ y=0.1$

1/0.1=10часов-время скорого на весь путь

Answer 2

Problem Analysis

We are given that a passenger train left point A and after three hours, an express train left point A as well. The express train caught up with the passenger train in the middle of the distance between points A and B. At the moment the express train arrived at point B, the passenger train had covered 13/16 of the total distance. We need to determine how much time the express train requires to cover the entire distance from point A to point B.

Solution

Let's assume the total distance between points A and B is represented by d.

We are given that the passenger train covers 13/16 of the total distance before the express train arrives at point B. Therefore, the passenger train covers (13/16) * d distance.

Since the express train catches up with the passenger train in the middle of the distance between points A and B, the passenger train has covered half of the total distance when the express train arrives at point B. Therefore, the distance covered by the passenger train is also equal to (1/2) * d.

From the given information, we can set up the following equation:

(13/16) * d = (1/2) * d

To find the time required for the express train to cover the entire distance, we need to determine the remaining distance that the passenger train has not covered. Subtracting the distance covered by the passenger train from the total distance gives us:

d - (1/2) * d = (3/16) * d

Therefore, the remaining distance that the express train needs to cover is (3/16) * d.

Since the express train covers the remaining distance in the same amount of time it took the passenger train to cover (13/16) * d, we can set up the following equation:

(3/16) * d = (13/16) * t

Simplifying the equation, we find:

t = (3/13) * d

Therefore, the express train requires (3/13) times the total distance to cover the entire distance from point A to point B.

Answer

The express train requires (3/13) times the total distance to cover the entire distance from point A to point B.

Let's calculate the time required for the express train to cover the entire distance using the given information.

Assuming the total distance between points A and B is 1 unit, the express train requires (3/13) units of time to cover the entire distance.

Please note that the actual time required will depend on the specific distance between points A and B.