Question

По двум параллельным железнодорожным путям в одном направлении следуют пассажирский и скорый поезда. Скорый поезд, двигаясь со скоростью 120 км/ч , догнал пассажирский поезд и прошел мимо него за 100 секунд. Найдите скорость пассажирского поезда, если его длинна составляет 800 метров, а длинна скорого поезда- 700 метров. Дайте ответ в км/ч со всеми расчетами и объяснениями

Answer 1

Пусть скорость пассажирского поезда х км/час
Скорый поезд догоняет пассажирский со скоростью 120 км/час
Скорость сближения (120-х) км/час

Время за которое скорый поезд догнал и прошел мимо 100с= 100/3600=1/36 час

путь который прошел скорый поезд это своя длина и длина пассажирского поезда

700 м+800 м=1500 м=1,5 км

Воспользуемся формулой:

$S=V*t$

Путь 1,5км
скорость (120-х) км/час
время 1/36ч

составим уравнение:

$1,5= \frac{120-x}{36} 1.5*36=120-x 54=120-x 120-54=x x=66$

Скорость пассажирского поезда 66 км/час

Answer 2

Problem Analysis

We are given that a passenger train and an express train are traveling in the same direction along two parallel railway tracks. The express train, traveling at a speed of 120 km/h, overtakes the passenger train and passes it in 100 seconds. We are asked to find the speed of the passenger train, given that its length is 800 meters and the length of the express train is 700 meters.

Solution

To solve this problem, we can use the concept of relative speed. The relative speed between the two trains is the difference in their speeds. When the express train overtakes the passenger train, the relative speed between them is equal to the sum of their speeds.

Let's denote the speed of the passenger train as v km/h. The relative speed between the two trains is then (120 - v) km/h.

We can calculate the distance traveled by the express train in 100 seconds. The distance traveled is equal to the sum of the lengths of the passenger train and the express train.

The distance traveled by the express train in 100 seconds is given by the formula:

Distance = Speed × Time

Substituting the values, we have:

Distance = (120 - v) × (100/3600) km

The distance traveled by the express train is equal to the sum of the lengths of the passenger train and the express train:

Distance = 800 meters + 700 meters = 1500 meters = 1.5 kilometers

Equating the two expressions for distance, we can solve for v:

(120 - v) × (100/3600) = 1.5

Simplifying the equation, we get:

(120 - v) × 0.027778 = 1.5

Dividing both sides of the equation by 0.027778, we have:

120 - v = 54.167

Subtracting 120 from both sides of the equation, we get:

-v = -65.833

Multiplying both sides of the equation by -1, we have:

v = 65.833

Therefore, the speed of the passenger train is approximately 65.833 km/h.

Answer

The speed of the passenger train is approximately 65.833 km/h.

Calculation Steps

- The relative speed between the passenger train and the express train is (120 - v) km/h. - The distance traveled by the express train in 100 seconds is (120 - v) × (100/3600) km. - The distance traveled by the express train is equal to the sum of the lengths of the passenger train and the express train, which is 1.5 kilometers. - Equating the two expressions for distance, we have (120 - v) × (100/3600) = 1.5. - Solving for v, we find that the speed of the passenger train is approximately 65.833 km/h.

Note: The sources provided did not contain specific information related to this problem. The solution is derived using mathematical principles and formulas.