Question

Расстояние между станциями А и В равно 120 км. Вслед за поездом, вышедшим из А в В, через 3ч в этом же направлении отправился второй поезд, скорость которого на 10км/ч больше скорости первого поезда. Известно, что первый поезд прибыл на станцию В на 2ч раньше, чем второй. За сколько часов пройдет путь от А до В второй поезд?

Answer 1

Пусть за х часов 1-ый поезд доехал до станции,

тогда за (х+2-3) часов 2-ой поезд доехал до станции.

Тогда:

120 / х + 10 = 120 / (х+2-3)

(120+10х) : х = 120 /(х-1)

Используя приём перекрёстного умножения, получаем:

120х = (120+10х)*(х-1)

120х = 120х-120+10хх-10х

120х = 110х-120+10хх

10х = 10хх-120

Каждую часть уравнения поделим на 10:

х = хх-12

Методом подбора находим, квадрат какого числа на 12 больше самого числа?

х=4

(х+2-3)=4-1=3 часа

Ответ:второй поезд доедет до станции за 3 часа.

Answer 2

Problem Analysis

We are given that the distance between stations A and B is 120 km. A train leaves station A and after 3 hours, another train, traveling in the same direction, leaves station A at a speed that is 10 km/h faster than the first train. We also know that the first train arrives at station B 2 hours before the second train. We need to determine how many hours it will take for the second train to travel from station A to station B.

Solution

Let's assume the speed of the first train is x km/h. Therefore, the speed of the second train is x + 10 km/h.

We can use the formula distance = speed × time to calculate the time it takes for each train to travel from station A to station B.

For the first train: - Distance = 120 km - Speed = x km/h - Time = 120 / x hours

For the second train: - Distance = 120 km - Speed = x + 10 km/h - Time = 120 / (x + 10) hours

We are given that the first train arrives at station B 2 hours before the second train. Therefore, the time taken by the first train minus the time taken by the second train is equal to 2 hours:

(120 / x) - (120 / (x + 10)) = 2

To solve this equation, we can cross-multiply and simplify:

(120(x + 10)) - 120x = 2(x)(x + 10)

Simplifying further:

120x + 1200 - 120x = 2x^2 + 20x

1200 = 2x^2 + 20x

2x^2 + 20x - 1200 = 0

Now we can solve this quadratic equation to find the value of x.

Calculation

Using the quadratic formula, we have:

x = (-b ± sqrt(b^2 - 4ac)) / (2a)

Where: - a = 2 - b = 20 - c = -1200

Substituting the values into the formula:

x = (-20 ± sqrt(20^2 - 4 * 2 * -1200)) / (2 * 2)

Simplifying:

x = (-20 ± sqrt(400 + 9600)) / 4

x = (-20 ± sqrt(10000)) / 4

x = (-20 ± 100) / 4

We have two possible values for x:

1. x = (-20 + 100) / 4 = 80 / 4 = 20 2. x = (-20 - 100) / 4 = -120 / 4 = -30

Since the speed of a train cannot be negative, we discard the second solution.

Therefore, the speed of the first train is 20 km/h, and the speed of the second train is 20 + 10 = 30 km/h.

To find the time taken by the second train to travel from station A to station B, we can substitute the speed of the second train into the formula:

Time = 120 / (30) = 4 hours

Therefore, the second train will take 4 hours to travel from station A to station B.

Answer

The second train will take 4 hours to travel from station A to station B.