Question

Пешеход идет по обочине дороги со скоростью 6 километров в час. Каждые 30 минут его обгоняет рейсовый автобус, а каждые 27/11 км мимо него проезжает встречный автобус. Найдите интервал движение автобусов, если известно, что он одинаковый в обоих направлениях. Скорости автобусов одинаковые.

Answer 1

Vп (скор автоб. попутная с пешеходом)
Vв (сокр автоб. встречая с пешеходом)
Vа (скорость автобуса)
Vп=Vв из усл.
Vп=Vа-6
Vв=Vа+6
Vа-6=Vа+6
(Sп/tдв)-6=(Sв/tдв)+6
где:
Sп расстояние пройдено авт. попутно
Sп.=6*1/2ч = 3 км.
Sв расстояние пройдено авт. встречн
27/11 км. из усл.
tдв. время движения (без учёта интервала)
3/tдв=(27/(11*tдв))+12
33=27+132*tдв.
6=132*tдв
tдв=1/22 ч.
интервал движения:
30мин =1/2 ч. - 1/22 ч. = 10/22 ч. = 5/11 ч.
для проверки:
Vавтобуса = 3/(1/22)=66км./ч.

Answer 2

Problem Analysis

We are given that a pedestrian is walking along the side of a road at a speed of 6 kilometers per hour. Every 30 minutes, a passenger bus overtakes the pedestrian, and every 27/11 kilometers, a bus traveling in the opposite direction passes by. We need to find the interval between the movements of the buses if their speeds are the same in both directions.

Solution

To find the interval between the movements of the buses, we need to determine the distance covered by the pedestrian during the time it takes for the buses to pass by.

Let's assume that the interval between the movements of the buses is 'x' kilometers. During this interval, the pedestrian is overtaken by the passenger bus and also has a bus traveling in the opposite direction pass by.

The time it takes for the passenger bus to overtake the pedestrian is 30 minutes, which is equal to 0.5 hours. During this time, the pedestrian covers a distance of 6 * 0.5 = 3 kilometers.

Similarly, the time it takes for the bus traveling in the opposite direction to pass by the pedestrian is equal to the time it takes for the pedestrian to cover a distance of 'x' kilometers at a speed of 6 kilometers per hour. This can be calculated using the formula: time = distance / speed. Therefore, the time taken is x / 6 hours.

Since the interval between the movements of the buses is the sum of the time taken for the passenger bus to overtake the pedestrian and the time taken for the bus traveling in the opposite direction to pass by, we can write the equation:

x = 0.5 + x / 6

To solve this equation, we can multiply both sides by 6 to eliminate the fraction:

6x = 3 + x

Simplifying the equation, we get:

5x = 3

Dividing both sides by 5, we find:

x = 3/5

Therefore, the interval between the movements of the buses is 3/5 kilometers.

Answer

The interval between the movements of the buses is 3/5 kilometers.