Question

Избушка на курьих ножках за 6 3/5 минуты 12 ра повернулась к лесу передом, к Ивану задом. К Ивану передом, к лесу задом избушка каждый раз поворачивалась медленнее в 2 1/5 раза. Сколько времени потребовалось избушке, чтобы 12 раз повернуться к Ивану передом?

Answer 1

Пусть Х времени она поворачивалась передом, тогда 2 1/2х поворачивалась задом,
12:6 3/5=12/1:33/5=12/1*5/33=60/33 время одного оборота, уравнение:
х+2 1/5х=60/33
3 1/5х=60/33
х=60/33:3 1/5=60/33:16/2=60/33*2/16
х=5/22 передом 1 раз
5/22*12=60/22=30/11=2 8/11 передом 12 раз
кажется так

Answer 2

Problem Analysis

We are given a problem where a house on chicken legs turns towards the forest in front and towards Ivan in the back. The house turns slower each time, and we need to determine how much time it takes for the house to turn towards Ivan 12 times.

Solution

To solve this problem, we need to break it down into steps and calculate the time it takes for each turn.

1. Calculate the time it takes for the house to turn towards Ivan the first time. 2. Calculate the time it takes for the house to turn towards Ivan the second time. 3. Repeat step 2 until we have calculated the time for all 12 turns. 4. Sum up the times for all 12 turns to get the total time.

Let's calculate the time for each turn step by step.

Step 1: Calculate the time for the first turn

According to the problem, the house turns towards Ivan the first time in 6 3/5 minutes.

Step 2: Calculate the time for the second turn

The house turns slower each time, in a ratio of 2 1/5. To calculate the time for the second turn, we need to multiply the time for the first turn by the ratio.

Time for the second turn = (Time for the first turn) * (Ratio)

Let's calculate the time for the second turn using the given values: Time for the second turn = (6 3/5 minutes) * (2 1/5)

To multiply mixed numbers, we need to convert them to improper fractions: 6 3/5 = (5 * 6 + 3) / 5 = 33/5 2 1/5 = (5 * 2 + 1) / 5 = 11/5

Time for the second turn = (33/5) * (11/5) = 363/25 minutes

Step 3: Calculate the time for the third turn

To calculate the time for the third turn, we need to multiply the time for the second turn by the ratio again.

Time for the third turn = (Time for the second turn) * (Ratio)

Let's calculate the time for the third turn using the given values: Time for the third turn = (363/25 minutes) * (2 1/5)

Again, we convert the mixed numbers to improper fractions: 2 1/5 = (5 * 2 + 1) / 5 = 11/5

Time for the third turn = (363/25) * (11/5) = 3993/125 minutes

Step 4: Repeat steps 2 and 3 for all 12 turns

We repeat steps 2 and 3 for a total of 12 turns. Each time, we multiply the time for the previous turn by the ratio.

Let's calculate the time for the remaining 9 turns using the given values: Time for the fourth turn = (3993/125 minutes) * (2 1/5) = 43823/625 minutes Time for the fifth turn = (43823/625 minutes) * (2 1/5) = 481053/3125 minutes Time for the sixth turn = (481053/3125 minutes) * (2 1/5) = 5291583/15625 minutes Time for the seventh turn = (5291583/15625 minutes) * (2 1/5) = 58207413/78125 minutes Time for the eighth turn = (58207413/78125 minutes) * (2 1/5) = 640281543/390625 minutes Time for the ninth turn = (640281543/390625 minutes) * (2 1/5) = 7043096973/1953125 minutes Time for the tenth turn = (7043096973/1953125 minutes) * (2 1/5) = 77474066703/9765625 minutes Time for the eleventh turn = (77474066703/9765625 minutes) * (2 1/5) = 852214733733/48828125 minutes Time for the twelfth turn = (852214733733/48828125 minutes) * (2 1/5) = 9374362071063/244140625 minutes

Step 5: Calculate the total time for all 12 turns

To calculate the total time for all 12 turns, we need to sum up the times for each turn.

Total time = Time for the first turn + Time for the second turn + ... + Time for the twelfth turn

Let's calculate the total time using the calculated values: Total time = (6 3/5 minutes) + (363/25 minutes) + (3993/125 minutes) + (43823/625 minutes) + (481053/3125 minutes) + (5291583/15625 minutes) + (58207413/78125 minutes) + (640281543/390625 minutes) + (7043096973/1953125 minutes) + (77474066703/9765625 minutes) + (852214733733/48828125 minutes) + (9374362071063/244140625 minutes)

To add fractions, we need to find a common denominator: Total time = (6 3/5 minutes) + (363/25 minutes) + (3993/125 minutes) + (43823/625 minutes) + (481053/3125 minutes) + (5291583/15625 minutes) + (58207413/78125 minutes) + (640281543/390625 minutes) + (7043096973/1953125 minutes) + (77474066703/9765625 minutes) + (852214733733/48828125 minutes) + (9374362071063/244140625 minutes) Total time = (6 * 25 + 3) / 5 + 363/25 + 3993/125 + 43823/625 + 481053/3125 + 5291583/15625 + 58207413/78125 + 640281543/390625 + 7043096973/1953125 + 77474066703/9765625 + 852214733733/48828125 + 9374362071063/244140625 minutes Total time = 150/5 + 363/25 + 3993/125 + 43823/625 + 481053/3125 + 5291583/15625 + 58207413/78125 + 640281543/390625 + 7043096973/1953125 + 77474066703/9765625 + 852214733733/48828125 + 9374362071063/244140625 minutes

Now, let's calculate the total time: Total time = 30 + 14.52 + 31.944 + 70.1568 + 154.57856 + 338.65088 + 745.36352 + 1639.564288 + 3603.1742976 + 7932.7436288 + 17435.61667456 + 38320.14434048 minutes

Therefore, the total time for the house to turn towards Ivan 12 times is approximately 77,772.3 minutes.

Please note that the above calculations are based on the given problem statement and the provided values.