Question

Электричка прошла мимо встречного товарного поезда, двигающегося с такой же скоростью и имеющего в пять раз большую длину, за время с t1=63 с. За какое время t2 электричка пройдёт мимо встречного пассажирского поезда, который в три раза длиннее электрички и едет вдвое быстрее? Ответ выразить в с с, округлив до целых. Считать, что время движения одного поезда мимо другого – это промежуток времени от момента, когда поравнялись их «головы», до момента, когда поравнялись их «хвосты».

Answer 1

Электричка проехала поезд за 63 с, хотя он был длиннее в 5 раз, значит электричка сама себя проезжает за 63/5=12.6с,
Чтобы проехать товарный поезд, который едет вдвое быстрее(значит времени потребуется меньше) и в три раза длиннее(значит в три раза болье понадобится времени), то электричке понадобится 12.6с/2*3=18.9 секунд.
Ответ: 18.9 секунд

Answer 2

Problem Analysis

We are given the following information: - A train passes a freight train moving at the same speed and five times its length in a time of t1 = 63 seconds. - We need to find the time t2 it takes for the train to pass a passenger train that is three times longer than the train and travels at twice the speed.

Let's solve this problem step by step.

Solution

To solve this problem, we can use the concept of relative speed. The relative speed between two objects moving in the same direction is the difference in their speeds.

Let's assume the speed of the train is v and the length of the train is l.

1. In the first scenario, the train passes the freight train. The relative speed between the train and the freight train is v - v = 0 (since they are moving at the same speed). The length of the freight train is 5l. The time taken to pass the freight train is given as t1 = 63 seconds.

2. In the second scenario, the train passes the passenger train. The relative speed between the train and the passenger train is v - 2v = -v (since the passenger train is moving in the opposite direction). The length of the passenger train is 3l. We need to find the time taken to pass the passenger train, which is denoted as t2.

To find t2, we can use the formula:

t2 = (length of the passenger train) / (relative speed)

Substituting the values, we have:

t2 = 3l / (-v)

Now, we need to find the value of v in terms of t1 and l.

From the first scenario, we know that the train passes the freight train in t1 seconds. The length of the freight train is 5l. Therefore, the speed of the train can be calculated as:

v = (5l) / t1

Substituting this value of v in the equation for t2, we have:

t2 = 3l / (-(5l / t1))

Simplifying the equation, we get:

t2 = -3t1 / 5

Since time cannot be negative, we take the absolute value of t2:

t2 = |(-3t1 / 5)|

Now, let's substitute the given value of t1 and solve for t2.

Calculation

Given: t1 = 63 seconds

Substituting the value of t1 in the equation for t2, we have:

t2 = |(-3 * 63 / 5)|

Calculating the value of t2, we get:

t2 = |(-189 / 5)|

Since we need to round the answer to the nearest whole number, the value of t2 is approximately:

t2 ≈ 38 seconds

Therefore, the train will take approximately 38 seconds to pass the passenger train.

Answer

The train will take approximately 38 seconds to pass the passenger train.

Note: The above solution assumes that the train and the passenger train are moving at constant speeds and there are no other factors affecting their motion.