Question

Из пункта A в пункт B Отправился пассажирский поезд,в то же время из пункта B пункт A отправился грузовой поезд.Скорость каждого из них на всем участке движения постоянна.Через 2 ч после того,как поезда встретились,расстояние между ними составило 280 км.Пассажирский поезд прибыл в пункт B через 9 ч ,а грузовой - в пункт A через 16 ч.Найдите скорость пассажирского поезда. Плиз,с объяснениями.

Answer 1

280/2=140 км в час суммарная скорость
✓(9*16)=12 часов ехали до встречи
12+9=21 час ехал пассажирский
12+16=28 ч ехал грузовой
21/28=0,75 скорости пассажирского
140/1,75=80 км в час пассажирский
80*0,75=60 км/ч грузовой
21*80=1680 км между пунктами

Answer 2

Problem Analysis

We have a passenger train traveling from point A to point B and a freight train traveling from point B to point A. The speeds of both trains are constant throughout the journey. After 2 hours of travel, the distance between the trains is 280 km. The passenger train arrives at point B after 9 hours, and the freight train arrives at point A after 16 hours. We need to find the speed of the passenger train.

Solution

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

We know that the distance traveled by an object is equal to its speed multiplied by the time taken. Using this information, we can set up the following equations:

1. For the passenger train: - Distance = Speed × Time - Distance from A to B = v × 9

2. For the freight train: - Distance = Speed × Time - Distance from B to A = u × 16

We also know that after 2 hours of travel, the distance between the trains is 280 km. This means that the sum of the distances traveled by both trains is equal to the total distance between them:

v × 2 + u × 2 = 280

Now we have a system of equations that we can solve to find the values of v and u.

Solving the Equations

Let's solve the system of equations using the given information.

1. Distance from A to B = v × 9 2. Distance from B to A = u × 16 3. v × 2 + u × 2 = 280

To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of substitution.

From equation 1, we can express u in terms of v: u = (Distance from B to A) / 16 = (v × 9) / 16

Substituting this value of u in equation 3, we get: v × 2 + ((v × 9) / 16) × 2 = 280

Simplifying the equation: 2v + (9v / 8) = 280

Multiplying through by 8 to eliminate the fraction: 16v + 9v = 2240

Combining like terms: 25v = 2240

Dividing both sides by 25: v = 2240 / 25

Calculating the value of v: v = 89.6 km/h

Therefore, the speed of the passenger train is 89.6 km/h.

Answer

The speed of the passenger train is 89.6 km/h.

Explanation

The speed of the passenger train can be found by setting up a system of equations using the given information. By solving the system of equations, we find that the speed of the passenger train is 89.6 km/h.