Question

Поїзд затримався у дорозі на 16 хв. і ліквідував запізнення на перегоні, довжина якого 80 км, збільшивши швидкість на 10 км/год. Яка швидкість руху потяга за розкладом?

Answer 1

Примем скорость поезда, с которой он должен был ехать, за х.
Составим уравнение времени (t = S/V).
80/х =(80/(х+10)) + (16/60).
80/х =(80/(х+10)) + (4/15).
Приведём к общему знаменателю:
80*15*(х+10) = 80*15*х + 4*х*(х+10).
1200х+12000 = 1200х + 4х² + 40х.
Получаем квадратное уравнение:
4х² + 40х - 12000 = 0   или, сократив на 4:
х² + 10х -3000 = 0.
Квадратное уравнение, решаем относительно x: Ищем дискриминант:
D=10^2-4*1*(-3000)=100-4*(-3000)=100-(-4*3000)=100-(-12000)=100+12000=12100;Дискриминант больше 0, уравнение имеет 2 корня:
x₁=(√12100-10)/(2*1)=(110-10)/2=100/2=50;x₂=(-√12100-10)/(2*1)=(-110-10)/2=-120/2=-60. Этот корень отбрасываем.
Ответ: V = 50 км/час.

Answer 2

Calculation of Train Speed

To calculate the train's speed according to the schedule, we need to consider the delay and the increased speed during the journey.

Given information: - Delay: 16 minutes - Length of the section: 80 km - Increased speed: 10 km/h

To find the train's speed according to the schedule, we can use the formula:

Speed = Distance / Time

Let's calculate the time it took for the train to cover the 80 km section at the increased speed:

Time = Distance / Speed

The original time it would have taken the train to cover the 80 km section at the scheduled speed can be calculated by subtracting the delay from the total time:

Original Time = Time + Delay

Finally, we can calculate the train's speed according to the schedule using the formula:

Scheduled Speed = Distance / Original Time

Let's calculate the scheduled speed of the train:

1. Calculate the time it took for the train to cover the 80 km section at the increased speed: - Distance: 80 km - Increased speed: 10 km/h

Time = 80 km / (Scheduled Speed + 10 km/h)

2. Calculate the original time it would have taken the train to cover the 80 km section at the scheduled speed: - Delay: 16 minutes

Original Time = Time + 16 minutes

3. Calculate the scheduled speed of the train: - Distance: 80 km - Original Time: Calculated in step 2

Scheduled Speed = 80 km / Original Time

Let's calculate the scheduled speed of the train using the given information.