Question

У дорожки стоит столб. Улитки Фрося, Муся и Кузя одновременно поползли от основания столба с постоянными скоростями. Фрося --- направо по дорожке, Муся --- налево по дорожке, а Кузя --- вверх по столбу. Скорость улитки Кузи на 2 см в минуту меньше скорости улитки Фроси, а скорость улитки Муси вдвое больше скорости улитки Кузи. Через час между Мусей и Фросей было 6 м 60 см. На какую высоту за этот час заполз Кузя?

Answer 1

Ответ:

180 см

Пошаговое объяснение:

VКузи - x

VФроси - x+2

VМуси - 2x

660 : 60 = 11 (V) - их общая скорость

2x + x+2 = 11

3x = 9

x = 3

60 * 3 = 180

Answer 2

Problem Analysis

We have three snails named Frose, Musya, and Kuzia. They start crawling simultaneously from the base of a pole. Frose crawls to the right along a track, Musya crawls to the left along the same track, and Kuzia crawls upward along the pole. We are given the following information: - Kuzia's speed is 2 cm per minute slower than Frose's speed. - Musya's speed is twice as fast as Kuzia's speed. - After one hour, there is a distance of 6 meters and 60 centimeters between Musya and Frose.

We need to determine the height Kuzia crawled up during this hour.

Solution

Let's assume Frose's speed is x cm per minute. Therefore, Kuzia's speed will be (x - 2) cm per minute, and Musya's speed will be 2(x - 2) cm per minute.

After one hour, the distance between Musya and Frose is 6 meters and 60 centimeters, which is equal to 660 cm.

To find the height Kuzia crawled up, we need to calculate the time it took for Musya and Frose to reach the distance of 660 cm.

Let's denote the time it took for Musya and Frose to reach the distance of 660 cm as t minutes.

The distance traveled by Musya in t minutes is 2(x - 2)t cm, and the distance traveled by Frose in t minutes is xt cm.

According to the problem, the sum of these distances is equal to 660 cm:

2(x - 2)t + xt = 660

Simplifying the equation:

2xt - 4t + xt = 660

3xt - 4t = 660

Factoring out t:

t(3x - 4) = 660

Dividing both sides by (3x - 4):

t = 660 / (3x - 4)

Now, we can calculate the height Kuzia crawled up in one hour. Kuzia's speed is (x - 2) cm per minute, so the height is:

Height = (x - 2) * 60

Let's solve this equation to find the value of x and then calculate the height Kuzia crawled up.

Calculation

To solve the equation t = 660 / (3x - 4), we need to find the value of x.

Using the given information that after one hour, the distance between Musya and Frose is 6 meters and 60 centimeters (660 cm), we can substitute t = 60 and 660 into the equation:

60 = 660 / (3x - 4)

Cross-multiplying:

60(3x - 4) = 660

Simplifying:

180x - 240 = 660

180x = 900

x = 5

Now that we have the value of x, we can calculate the height Kuzia crawled up:

Height = (x - 2) * 60 = (5 - 2) * 60 = 3 * 60 = 180 cm

Therefore, Kuzia crawled up to a height of 180 cm during this hour.

Answer

Kuzia crawled up to a height of 180 cm during this hour.

Note: The solution provided above is based on the given information and calculations.