Question

От пионерского лагеря до города путь идёт сначала под гору, а затем горизонтально. Пионер проехал на велосипеде путь под гору со скоростью 12 км в час, а горизонтальный путь — со скоростью 9 км в час и прибыл в город через 55 мин. после выезда из лагеря. Обратно он проехал горизонтальный путь со скоростью 8 км в час, а на подъёме шёл со скоростью 4 км в час и прибыл в лагерь через 11/2 часа после выезда из города. Сколько километров от лагеря до города?

Answer 1

1)12+9=21 км
2)21+8=29км
3)29+4=33 км-от лагеря до города

Answer 2

Problem Analysis

The problem states that a pioneer travels from a camp to a city. The path consists of an uphill section followed by a horizontal section. The pioneer rides a bicycle uphill at a speed of 12 km/h and travels horizontally at a speed of 9 km/h. The pioneer arrives in the city 55 minutes after leaving the camp. On the return journey, the pioneer travels horizontally at a speed of 8 km/h and uphill at a speed of 4 km/h. The pioneer arrives back at the camp 1.5 hours after leaving the city. We need to determine the distance between the camp and the city.

Solution

Let's assume the distance between the camp and the city is d kilometers.

On the journey from the camp to the city: - The pioneer travels uphill at a speed of 12 km/h, so the time taken for the uphill section is d/12 hours. - The pioneer then travels horizontally at a speed of 9 km/h, so the time taken for the horizontal section is d/9 hours. - The total time taken for the journey from the camp to the city is 55 minutes, which is equal to 55/60 = 11/12 hours.

On the return journey from the city to the camp: - The pioneer travels horizontally at a speed of 8 km/h, so the time taken for the horizontal section is d/8 hours. - The pioneer then travels uphill at a speed of 4 km/h, so the time taken for the uphill section is d/4 hours. - The total time taken for the return journey from the city to the camp is 1.5 hours.

We can set up the following equation based on the given information:

(d/12) + (d/9) = 11/12 + d/8 + d/4

To solve this equation, we can multiply through by the least common multiple (LCM) of the denominators, which is 36:

3d + 4d = 33 + 9d + 18d

7d = 33 + 27d

27d - 7d = 33

20d = 33

d = 33/20

Therefore, the distance between the camp and the city is 33/20 kilometers.

Answer

The distance between the camp and the city is 33/20 kilometers.