Question

Решите задачу. На путь между двумя деревнями пешеход затратил на 4 часа 30 минут больше, чем мотоциклист. Скорость мотоциклиста 40 км/ч, скорость пешехода составляет 0,1 скорости мотоциклиста. Найдите расстояние между деревнями.

Answer 1

Problem Analysis

We are given that a pedestrian took 4 hours and 30 minutes longer than a motorcyclist to travel between two villages. The speed of the motorcyclist is 40 km/h, and the speed of the pedestrian is 0.1 times the speed of the motorcyclist. We need to find the distance between the villages.

Solution

Let's assume the distance between the villages is d km.

The time taken by the motorcyclist to travel the distance d is given by: time_motorcyclist = d / speed_motorcyclist

The time taken by the pedestrian to travel the distance d is given by: time_pedestrian = d / speed_pedestrian

Given that the pedestrian took 4 hours and 30 minutes longer than the motorcyclist, we can write the equation: time_pedestrian = time_motorcyclist + 4 hours and 30 minutes

Converting 4 hours and 30 minutes to hours, we have: time_pedestrian = time_motorcyclist + 4.5 hours

Substituting the values of time_pedestrian, time_motorcyclist, speed_pedestrian, and speed_motorcyclist, we get: (d / (0.1 * 40)) = (d / 40) + 4.5

Simplifying the equation, we have: d / 4 = d / 40 + 4.5

Multiplying both sides of the equation by 40, we get: 10d = d + 180

Subtracting d from both sides of the equation, we get: 9d = 180

Dividing both sides of the equation by 9, we get: d = 20

Therefore, the distance between the villages is 20 km.

Answer

The distance between the two villages is 20 km.