Question

Поїзд затриманий на 1 годину, на перегоні 200 км надолужує втрачений час, збільшивши швидкість на 10 км./год. яка початкова швидкість поїзда.

Answer 1

Нехай початкова швидкість поїзда - х.    ⇒
200/(х+10)+1=200/х
200x+x*(x+10)=200*(x+10)
200x+x²+10x=200x+2000
x²+10x-2000=0   D=8100
x₁=40     x₂=-50 ∉
Відповідь: початкова швидкість поїзда 40 км/ч.

Answer 2

Calculation of Initial Speed of the Train

To calculate the initial speed of the train, we can use the information provided. Let's break down the problem step by step:

1. The train is delayed by 1 hour. 2. During this delay, the train covers a distance of 200 km. 3. To make up for the lost time, the train increases its speed by 10 km/h.

To find the initial speed of the train, we need to determine the time it would take to cover the 200 km at the increased speed and then subtract the 1-hour delay.

Let's calculate the time it takes to cover 200 km at the increased speed:

Time = Distance / Speed

Time = 200 km / (Initial Speed + 10 km/h)

Now, we know that the train is delayed by 1 hour. So, the total time taken to cover the 200 km at the increased speed is 1 hour more than the time taken at the initial speed.

Time at increased speed = Time at initial speed + 1 hour

Substituting the values, we get:

200 km / (Initial Speed + 10 km/h) = 200 km / Initial Speed + 1 hour

To solve this equation, we can cross-multiply:

200 km * Initial Speed + 2000 km/h = 200 km * (Initial Speed + 10 km/h)

Expanding the equation:

200 km * Initial Speed + 2000 km/h = 200 km * Initial Speed + 2000 km/h

The equation simplifies to:

200 km * Initial Speed = 200 km * Initial Speed

This equation shows that the initial speed of the train does not affect the time taken to cover the 200 km at the increased speed. Therefore, we cannot determine the initial speed of the train based on the given information.

Please note that this calculation assumes a constant speed throughout the journey and does not take into account other factors that may affect the train's speed or delays.

If you have any further questions, feel free to ask!