Question

1.Крестьянин отправился пешком из села в город .возвращаясь обратно,он первую половину пути проехал на волах,которые шли в 2 раза медленнее,чем крестьянин шел пешком ,а вторую половину пути на лошади,скорость которой была в 2 раза больше скорости крестьянина 2.через сколько часов крестьянин должен был пересесть на лошадь,чтобы затратить на обратный путь столько же времени ,сколько на путь в город ,если от села до города 36 км ,а скорость крестьянина была 4 км/ч

Answer 1

36:4=9 ч - шел пешком
36:2=18 км - половина пути
18:2=9 ч - ехал на волах,( столько  же времени шел пешком)
4*2=8 км\ч - скорость лошади
18:8=2 1/4 ч==>2ч15 мин - ехал на лошади
9ч+2 ч15мин=11ч15 мин - время на обратном пути
11ч15мин - 9ч =2ч15 мин - больше времени ушло на обратный путь
 Пусть х час - время поездки на волах, чтобы успеть
(9-х) час - время поездки на лошади
2х+8(9-х)=36
6х=36
х=6(час) - через 6 часов должен был пересесть на лошадь.
Ответ: На волах ехал столько же времени, сколько шел пешком;
через 6 часов должен был пересесть на лошадь.

Answer 2

Problem Analysis

A peasant is traveling from a village to a city on foot. On the return journey, he travels the first half of the distance on oxen, which move at half his walking speed. He then travels the second half of the distance on a horse, which moves at twice his walking speed. The question is how many hours the peasant should have spent on the horse to spend the same amount of time on the return journey as he did on the journey to the city. The distance from the village to the city is 36 km, and the peasant's walking speed is 4 km/h.

Solution

To solve this problem, we need to find the time it takes for the peasant to travel from the village to the city on foot, and then find the time it takes for the peasant to travel back from the city to the village on the horse. We can then equate these two times to find the time the peasant should spend on the horse.

Let's calculate the time it takes for the peasant to travel from the village to the city on foot:

Distance: The distance from the village to the city is 36 km.

Walking speed: The peasant's walking speed is 4 km/h.

Using the formula `time = distance / speed`, we can calculate the time it takes for the peasant to travel from the village to the city on foot:

Time on foot: `time_on_foot = distance / walking_speed = 36 km / 4 km/h = 9 hours`.

Now let's calculate the time it takes for the peasant to travel back from the city to the village on the horse:

Distance: The distance from the city to the village is also 36 km.

Horse speed: The horse's speed is twice the peasant's walking speed, which is 2 * 4 km/h = 8 km/h.

Using the formula `time = distance / speed`, we can calculate the time it takes for the peasant to travel back from the city to the village on the horse:

Time on horse: `time_on_horse = distance / horse_speed = 36 km / 8 km/h = 4.5 hours`.

To spend the same amount of time on the return journey as he did on the journey to the city, the peasant should spend 9 hours in total. Since the peasant has already spent 4.5 hours on the horse, he should spend an additional 4.5 hours on the horse to make the total time equal to 9 hours.

Therefore, the peasant should have spent 4.5 hours on the horse to spend the same amount of time on the return journey as he did on the journey to the city.

Answer

The peasant should have spent 4.5 hours on the horse to spend the same amount of time on the return journey as he did on the journey to the city.

Please let me know if you need any further clarification.