Question

Очень надо пожалуйста полное решение!Путь от А до В пассажирский поезд проходит на 3 часа 12 минут быстрее товарного. За то время, что товарный поезд проходит путь от А до В, пассажирский проходит на 288 км больше. Если скорость каждого поезда увеличить на 10 км/ч, то пассажирский пройдет от А до В на 2 часа 24 минуты быстрее товарного. Определить расстояние от А до В.

Answer 1

Ответ: 360 км.

Пошаговое объяснение:

Пусть расстояние между А и В равно z км, а скорость пассажирского и товарного поездов равна х км/ч и у км/ч соответственно. Тогда время, затраченное пассажирским поездом на преодоления пути равно z/x (ч), а товарным — z/y (ч), что на 3+12/60 ч больше по условию. Имеем первое уравнение системы: $\frac{z}{y} - \frac{z}{x} =3 \frac{1}{5}$

За z/y (ч) пассажирский поезд проедет (z+288) км. Имеем второе уравнение системы: $x\frac{z}{y} = z + 288$

После повышения скорости на 10 км/ч пассажирский поезд потратит на путь (z/(x+10)) ч, а товарный — (z/(y+10)) ч, что на 2+24/60 ч больше по условию. Имеем третье уравнение системы:

$\frac{z}{y+10} - \frac{z}{x+10} = 2\frac{2}{5}$

Answer 2

Problem Analysis

We are given that the passenger train takes 3 hours and 12 minutes less than the freight train to travel from point A to point B. Additionally, during the time it takes the freight train to travel from A to B, the passenger train travels an additional 288 km. If the speed of both trains is increased by 10 km/h, the passenger train will take 2 hours and 24 minutes less than the freight train to travel from A to B. We need to determine the distance from A to B.

Solution

Let's assume the speed of the freight train is x km/h and the speed of the passenger train is y km/h.

From the given information, we can form the following equations:

Equation 1: The time taken by the passenger train is 3 hours and 12 minutes (or 3.2 hours) less than the time taken by the freight train. Equation 2: The distance traveled by the passenger train is 288 km more than the distance traveled by the freight train. Equation 3: If the speed of both trains is increased by 10 km/h, the passenger train will take 2 hours and 24 minutes (or 2.4 hours) less than the freight train.

Let's solve these equations step by step.

Equation 1: Time Difference

The time difference between the passenger train and the freight train is given as 3 hours and 12 minutes (or 3.2 hours). We can write this as:

Time taken by passenger train - Time taken by freight train = 3.2 hours

The time taken by each train can be calculated using the formula: Time = Distance / Speed.

Let's assume the distance from A to B is d km.

For the passenger train, the time taken is (d + 288) / y. For the freight train, the time taken is d / x.

Substituting these values into the equation, we get:

(d + 288) / y - d / x = 3.2

Equation 2: Distance Difference

The distance traveled by the passenger train is 288 km more than the distance traveled by the freight train. We can write this as:

Distance traveled by passenger train - Distance traveled by freight train = 288 km

Substituting the distances into the equation, we get:

(d + 288) - d = 288

Equation 3: Increased Speed Time Difference

If the speed of both trains is increased by 10 km/h, the passenger train will take 2 hours and 24 minutes (or 2.4 hours) less than the freight train. We can write this as:

Time taken by passenger train (with increased speed) - Time taken by freight train (with increased speed) = 2.4 hours

Using the same formula as before, the time taken by each train with increased speed is:

For the passenger train: d / (y + 10) For the freight train: d / (x + 10)

Substituting these values into the equation, we get:

d / (y + 10) - d / (x + 10) = 2.4

Now we have a system of three equations with three unknowns (d, x, and y). Let's solve this system of equations to find the values.

Solving the Equations

To solve the system of equations, we can use substitution or elimination. Here, we'll use the substitution method.

From Equation 2, we have d + 288 = 288. Simplifying this equation, we get d = 0.

Substituting this value of d into Equations 1 and 3, we get:

(0 + 288) / y - 0 / x = 3.2 -> 288 / y = 3.2 -> y = 90

0 / (90 + 10) - 0 / x + 10 = 2.4 -> 0 - 0 / x + 10 = 2.4 -> 10 / x + 10 = 2.4 -> 10 / x = 2.4 - 10 -> 10 / x = -7.6 -> x = -10 / 7.6

Since the speed cannot be negative, we discard this solution.

Therefore, the speed of the freight train is x = -10 / 7.6 km/h and the speed of the passenger train is y = 90 km/h.

Now, we need to find the distance from A to B. We can use any of the three equations to find the distance. Let's use Equation 2:

Distance traveled by passenger train - Distance traveled by freight train = 288 km

Substituting the values of y and x, we get:

(d + 288) - d = 288 -> 288 = 288

This equation is true for any value of d. Therefore, the distance from A to B can be any value.

In conclusion, the distance from A to B is not determined by the given information.