Question

За лучший ответ 100 баллов --------------------------- По графику поезд проходит перегон А в В 120 км. с одной и той же скоростью.Первый раз поезд прошел полпути с этой скоростью остановился на 5 минут;чтобы во-время прийти в В,ему пришлось остальные полпути идти на 10 км/ч быстрее.Второй раз поезд застрял на пол пути уже на 9 минут.С какой скоростью он должен был идти оставшуюся часть пути,чтобы прибыть в В по расписанию? ----------------------------- Можете все расписать!!!и с проверкой !решение полное,расписанное,чтоб я поняла!За лучший ответ 100 баллов!!

Answer 1

 первый случай 
x - обычная скорость поезда
60/x=60/(x+10)+1/12
решаем квадратное уравнение, откужа х=80км/ч - обычная скорость поезда
второй случай
х - скорость, которая должна быть
60/80=60/x+3/20
откуда х=100км/ч - с такой скоростью должен идти поезд

Answer 2

Problem Analysis

We are given that a train travels from point A to point B, a distance of 120 km, at a constant speed. The train initially travels half the distance at this speed, then stops for 5 minutes, and finally completes the remaining half of the distance at a speed that is 10 km/h faster. On another occasion, the train gets stuck halfway for 9 minutes. We need to determine the speed at which the train must travel for the remaining distance in order to arrive at point B on time.

Solution

Let's assume the initial speed of the train is x km/h. According to the problem, the train travels half the distance at this speed, then stops for 5 minutes, and finally completes the remaining half of the distance at a speed that is 10 km/h faster.

To find the initial speed of the train, we can set up the following equation:

Time taken to travel half the distance at speed x + 5 minutes = Time taken to travel the remaining half of the distance at speed (x + 10)

The time taken to travel a certain distance can be calculated using the formula:

Time = Distance / Speed

Let's calculate the time taken to travel half the distance at speed x:

Time taken to travel half the distance = (120 km / 2) / x = 60 km / x

Now, let's calculate the time taken to travel the remaining half of the distance at speed (x + 10):

Time taken to travel the remaining half of the distance = (120 km / 2) / (x + 10) = 60 km / (x + 10)

According to the problem, the time taken to travel half the distance at speed x plus 5 minutes is equal to the time taken to travel the remaining half of the distance at speed (x + 10):

60 km / x + 5 minutes = 60 km / (x + 10)

To solve this equation, we can cross-multiply:

60(x + 10) = 60x + 5(x + 10)

Simplifying the equation:

60x + 600 = 60x + 5x + 50

60x - 60x - 5x = 50 - 600

-5x = -550

Dividing both sides by -5:

x = 110

Therefore, the initial speed of the train is 110 km/h.

Now, we need to find the speed at which the train must travel for the remaining distance in order to arrive at point B on time.

Let's assume the speed for the remaining distance is y km/h. The time taken to travel the remaining half of the distance at speed y can be calculated as:

Time taken to travel the remaining half of the distance = (120 km / 2) / y = 60 km / y

According to the problem, the train gets stuck halfway for 9 minutes. Therefore, the total time taken to travel the remaining half of the distance is:

Time taken to travel the remaining half of the distance + 9 minutes = Time taken to travel half the distance at speed 110

Substituting the values:

60 km / y + 9 minutes = 60 km / 110

To solve this equation, we can cross-multiply:

60(110) = 60y + 9y

Simplifying the equation:

6600 = 69y

Dividing both sides by 69:

y = 95.65

Therefore, the train must travel at a speed of approximately 95.65 km/h for the remaining distance in order to arrive at point B on time.

Answer

To arrive at point B on time, the train must travel at a speed of approximately 95.65 km/h for the remaining distance.

Please note that the solution provided is based on the information given in the problem statement.