Question

Встретившись возле железнодорожного переезда, Фокс и Форд договорились поставить эксперимент: как только первый вагон товарного поезда поравняется с ними, то они начнут двигаться вдоль поезда в противоположных направлениях со скоростью V = 6км}ч и будут считать вагоны, пока не пройдут 100 метров. В результате эксперимента Фокс насчитал 10 вагонов, а Форд – 20 вагонов. Определите скорость поезда, считая, что она была постоянной и большей, чем скорость экспериментаторов. Ответ выразите в км ч, округлив до целых. Товарный поезд имеет более 20 вагонов.

Answer 1

v1 = скорость поезда

v = 6км/ч скорость человека

S1=0.1 км

N=10

для идущего вдоль поезда общая скорость = 

V=v1-v

 S2=N*s Расстояние = (количество вагонов * длину каждого вагона)

t=S2/V=N*s/(v1-v)

Для идущего против движения поезда

V=v1+v

S3=2*N*s

t2=2*N*s/(v1+v)

запишем уравнение приравняв время

N*s/(v1-v)=2*N*s/(v1+v)

1/((v1-v)*2)=1/(v1+v)

2v1-2v=v1+v

v1=3v

v1=3*6=18 км/ч скорость поезда

найдем длину вагонов

время наблюдения t1=S1/v=0.1/6=0.017 часа

Длина поезда, которую увидел шедший вдоль движения

S2=(v1-v)*t=(18-6)*0.02=0.204 км =204м

Длина одного вагона

s=S2/N=204/10=20.4 метрa длина одного вагона.

Answer 2

Problem Analysis

In this problem, Fox and Ford conducted an experiment near a railway crossing. They agreed to start moving in opposite directions along the train as soon as the first wagon of a freight train reached them. They counted the number of wagons they passed until they had traveled 100 meters. Fox counted 10 wagons, while Ford counted 20 wagons. We need to determine the speed of the train, assuming it was constant and greater than the speed of the experimenters.

Solution

Let's assume the speed of the train is V km/h. Since both Fox and Ford counted the number of wagons they passed until they traveled 100 meters, we can set up the following equation:

Distance traveled by Fox = Distance traveled by Ford

The distance traveled by Fox is equal to the speed of Fox multiplied by the time it took to travel 100 meters. Similarly, the distance traveled by Ford is equal to the speed of Ford multiplied by the time it took to travel 100 meters. Since the time taken by both experimenters is the same, we can equate the two distances:

Speed of Fox × Time = Speed of Ford × Time

Simplifying the equation, we get:

Speed of Fox = Speed of Ford

Since both Fox and Ford counted different numbers of wagons, we can conclude that the speed of the train is not equal to the speed of either experimenter. Therefore, the speed of the train is greater than the speed of both Fox and Ford.

To determine the speed of the train, we can use the information given in the problem: Fox counted 10 wagons and Ford counted 20 wagons. Since both experimenters traveled the same distance, we can set up the following equation:

Speed of train × Time = Number of wagons × Length of each wagon

Simplifying the equation, we get:

Speed of train = (Number of wagons × Length of each wagon) / Time

We are given that the length of each wagon is not specified, but it is mentioned that the freight train has more than 20 wagons. Therefore, we can assume that the number of wagons is greater than 20.

Now, let's calculate the speed of the train using the given information.

Calculation

Given: - Fox counted 10 wagons. - Ford counted 20 wagons. - Distance traveled by both experimenters = 100 meters.

We can calculate the speed of the train using the formula:

Speed of train = (Number of wagons × Length of each wagon) / Time

Since the length of each wagon is not specified, we can assume a standard length of 10 meters for each wagon.

Substituting the values into the formula:

Speed of train = (20 wagons × 10 meters) / (100 meters)

Simplifying the equation:

Speed of train = 2000 meters / 100 meters = 20

Therefore, the speed of the train is 20 km/h.

Answer

The speed of the train, assuming it was constant and greater than the speed of the experimenters, is 20 km/h.

Note: The assumption made for the length of each wagon is arbitrary, as the problem does not provide this information.