Question

Сельчанин может добраться от своего дома до города двумя способами. В первом случае ему придется 2 часа идти пешком и 3 часа ехать автобусом, и он преодолеет в общей сложности 113 км. Во втором случае ему придется 1 час 30 минут идти пешком и 5 часов ехать автобусом (в обоих случаях автобусы движутся с одинаковыми скоростями) . Длина второй дороги равна 181 км. С какой скоростью сельчанин ходит?

Answer 1

Два неизвестных - скорости пешехода -Х  и автобуса.- У.
Пишем два уравнения.
1) 2*Х + 3*У = 113 км - првый вариант
2) 1,5*Х + 5*У = 181 км - второй вариант
Решим методом Гаусса -  приводим уравнения к общему коэффициенту при Х.
3) 3*Х+ 4,5*У = 113 *1,5 = 169,5 - умножили на 1,5
4) 3*Х + 10*У = 181*2 = 362  - умножили на 2.
Вычитаем уравнения - 4) - 3)
5) 5,5*У = 362 - 169,5 = 192,5
Находим неизвестное - У
6) У = 192,5 : 5,5 = 35 км/ч - скорость автобуса - ОТВЕТ
Подставим в ур. 1) (можно и в ур. 2)
7) 2*Х + 3*35 = 113
Находим неизвестное - Х
8) 2*Х =: 113 - 105 = 8
8а) Х = 8 : 2 = 4 км/ч - скорость пешехода - ОТВЕТ

Answer 2

Calculation of Walking Speed

To determine the walking speed of the villager, we can use the information provided in the question. The villager has two options for reaching the city:

1. Option 1: Walking for 2 hours and taking a 3-hour bus ride, covering a total distance of 113 km. 2. Option 2: Walking for 1 hour and 30 minutes and taking a 5-hour bus ride, covering a total distance of 181 km.

Let's calculate the walking speed of the villager.

For Option 1: - Walking time: 2 hours - Distance covered by walking: Unknown - Bus ride time: 3 hours - Distance covered by bus: Unknown - Total distance: 113 km

For Option 2: - Walking time: 1 hour and 30 minutes - Distance covered by walking: Unknown - Bus ride time: 5 hours - Distance covered by bus: Unknown - Total distance: 181 km

To find the walking speed, we need to determine the distance covered by walking in each option. We can set up a proportion using the given information:

Option 1: Walking time / Total time = Distance covered by walking / Total distance

2 hours / (2 hours + 3 hours) = Distance covered by walking / 113 km

Option 2: Walking time / Total time = Distance covered by walking / Total distance

1.5 hours / (1.5 hours + 5 hours) = Distance covered by walking / 181 km

Now, let's solve these proportions to find the distance covered by walking in each option.

For Option 1: 2 hours / (2 hours + 3 hours) = Distance covered by walking / 113 km

Simplifying the proportion: 2 / 5 = Distance covered by walking / 113

Cross-multiplying: 2 * 113 = 5 * Distance covered by walking

Distance covered by walking = (2 * 113) / 5 = 226 / 5 = 45.2 km

For Option 2: 1.5 hours / (1.5 hours + 5 hours) = Distance covered by walking / 181 km

Simplifying the proportion: 1.5 / 6.5 = Distance covered by walking / 181

Cross-multiplying: 1.5 * 181 = 6.5 * Distance covered by walking

Distance covered by walking = (1.5 * 181) / 6.5 = 271.5 / 6.5 = 41.77 km

Therefore, the villager walks approximately 45.2 km in Option 1 and 41.77 km in Option 2.

Now, let's calculate the walking speed by dividing the distance covered by walking by the walking time in each option.

For Option 1: Walking speed = Distance covered by walking / Walking time

Walking speed = 45.2 km / 2 hours = 22.6 km/h

For Option 2: Walking speed = Distance covered by walking / Walking time

Walking speed = 41.77 km / 1.5 hours = 27.85 km/h

Therefore, the villager walks at a speed of approximately 22.6 km/h in Option 1 and 27.85 km/h in Option 2.