Question

Поезд был задержан в пути на 12 минут, а затем на расстоянии 60 км наверстал потерянное время, увеличив скорость на 15 км/час. Найти первоначальную скорость поезда.

Answer 1

Пусть первоначальная скорость хкм/час, тогда новая скорость (х+15)км/час. Вычислим время: 60/х час. и 60/(х+15) час. Переведём 12 мин. в часы, это будет 1/5 часа. Составим уравнение: 60/х=60/( х+15) +1/5, общий знаменатель 5х (х+15), найдём дополнительные множители это 5(15+х) , 5х, х (х+15). Когда умножим, то получится 300(х+15)=60*5х+х (х+15), раскроем скобки и приведём подобные, получим: х в квадрате плюс 15х минус 4500 равно 0. Найдём корни 

Answer 2

Calculation of Initial Speed of the Train

To find the initial speed of the train, we can use the information provided. The train was initially delayed by 12 minutes and then made up for the lost time by increasing its speed by 15 km/h over a distance of 60 km.

Let's assume the initial speed of the train as x km/h.

The time taken to cover a distance of 60 km at the initial speed would be 60/x hours.

The time taken to cover the same distance at a speed increased by 15 km/h would be 60/(x+15) hours.

According to the given information, the train made up for the lost time, which means the time taken at the initial speed plus the time taken at the increased speed should be equal to the total time taken, which is 12 minutes or 12/60 hours.

So, we can set up the equation:

60/x + 60/(x+15) = 12/60

To solve this equation, we can multiply through by x(x+15) to eliminate the denominators:

60(x+15) + 60x = 12(x)(x+15)

Simplifying the equation:

60x + 900 + 60x = 12x^2 + 180x

Rearranging the equation:

12x^2 + 180x - 120x - 900 = 0

12x^2 + 60x - 900 = 0

Dividing through by 12:

x^2 + 5x - 75 = 0

Now, we can solve this quadratic equation to find the value of x, which represents the initial speed of the train.

Using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 1, b = 5, and c = -75.

Calculating the discriminant (b^2 - 4ac):

Discriminant = 5^2 - 4(1)(-75) = 25 + 300 = 325

Since the discriminant is positive, there are two real solutions for x.

Using the quadratic formula:

x = (-5 ± √325) / 2

Calculating the values of x:

x1 = (-5 + √325) / 2 ≈ 7.18 km/h x2 = (-5 - √325) / 2 ≈ -12.18 km/h

Since the speed of the train cannot be negative, we can discard the negative value.

Therefore, the initial speed of the train is approximately 7.18 km/h.