Question

Поезд должен пройти 1680 км за определенное время.на половине пути он был задержан у семафора на 1 ч и,для того чтобы прибыть к месту назначения в срок,увеличил скорость на 4 км/ч. сколько часов поезд находился в пути?

Answer 1

Скорость на первой половине пути х км/ч
скорость на второй половине пути х+4 км/ч
Время прохождения первой половины пути 1680:2/х часов=840/х часов
Время прохождения второй половины пути с учётом задержки на 1 час
равно 1680:2/(х+4) +1=840/(х+4) +1
Составляем уравнение:
$\frac{840}{x} = \frac{840}{x+4} +1|*x(x+4) \neq 0\\\\840(x+4)=840x+x(x+4)\\840x+3360=840x+x^2+4x\\x^2+4x-3360=0\\D=4^2-4*1(-3360)=13456=116^2\\x_1=(-4+116):2=56\\x_2=(-4-116):2=-60$

x2∉N
x=56(км/ч)-первоначальная скорость поезда
1680:56=30(ч)-находился в пути поезд

Answer 2

Problem Analysis

We are given that a train needs to travel a distance of 1680 km within a certain time frame. The train is delayed by 1 hour at a signal halfway through the journey. To arrive at the destination on time, the train increases its speed by 4 km/h. We need to determine how many hours the train was in transit.

Solution

To solve this problem, we can break it down into two parts: the time taken to cover the first half of the distance and the time taken to cover the second half of the distance.

Let's assume the original speed of the train is x km/h. Since the train is delayed by 1 hour at the halfway point, the time taken to cover the first half of the distance is (840 km / x km/h) + 1 hour.

To arrive at the destination on time, the train increases its speed by 4 km/h. Therefore, the speed for the second half of the distance is (x + 4) km/h. The time taken to cover the second half of the distance is (840 km / (x + 4) km/h).

To find the total time taken for the journey, we add the time taken for the first half and the time taken for the second half:

Total time = (840 km / x km/h) + 1 hour + (840 km / (x + 4) km/h)

Now we can solve this equation to find the total time taken by the train.

Calculation

Let's calculate the total time taken by the train using the given information.

Given: - Distance: 1680 km - Delay at the halfway point: 1 hour - Increase in speed: 4 km/h

We need to find the total time taken by the train.

Using the equation derived above, we have:

Total time = (840 km / x km/h) + 1 hour + (840 km / (x + 4) km/h)

Substituting the given values, we get:

Total time = (840 km / x km/h) + 1 hour + (840 km / (x + 4) km/h)

Now we can solve this equation to find the total time taken by the train.

Answer

The train was in transit for a total of (840 km / x km/h) + 1 hour + (840 km / (x + 4) km/h).

Please note that we need the value of the original speed of the train (x km/h) to calculate the total time taken. If you provide the value of x km/h, I can calculate the total time for you.