Question

По бортику круглого цветочного горшка ползут гусеница и улитка в одном направлении с постоянными скоростями. Когда за ними начал наблюдать Женя, они были в диаметрально противоположных точках бортика. Время от времени гусеница обгоняет улитку. Третий обгон произошёл через 9 минут после начала наблюдения. Через сколько минут после третьего обгона произойдёт четвёртый? Запишите решение и ответ. ​

Answer 1

Ответ:

Тк они были в диаметрально противоположных точках, то гусенице, чтобы догнать улитку, нужно проползти вдвое меньшее расстояние на 1м круге, а значит и затратить вдвое меньше времени (из t= S\V), чтобы нагнать улитку.

Т.к улитку догоняли 3 раза 1 из которых вдвое меньше других, то 2 + 0.5(неполный круг) = 2.5 раза (круга)

11 минут = 660 сек

660\2.5=264 сек = 4.4 минуты - понадобится улитке, чтобы совершить сл обгон (Время проползания 1го круга

Пошаговое объяснение:

Answer 2

To solve this problem, let's break it down step by step.

Given information:

- A caterpillar and a snail are crawling along the edge of a round flower pot in the same direction. - They start at diametrically opposite points on the edge of the pot. - The caterpillar occasionally overtakes the snail. - The third overtaking occurs 9 minutes after the start of the observation.

Approach:

1. Let's assume the circumference of the flower pot is C. 2. Let's assume the speed of the caterpillar is c (in units of distance per minute) and the speed of the snail is s (in units of distance per minute). 3. Since the caterpillar overtakes the snail, its speed must be greater than the snail's speed: c > s. 4. The time it takes for the caterpillar to complete one full lap around the pot is C/c minutes. 5. The time it takes for the snail to complete one full lap around the pot is C/s minutes. 6. The time it takes for the caterpillar to overtake the snail is the difference between the time it takes for the caterpillar to complete one lap and the time it takes for the snail to complete one lap: C/c - C/s minutes. 7. We are given that the third overtaking occurs 9 minutes after the start of the observation, so we can set up the following equation: C/c - C/s = 9.

Solving the equation:

To solve the equation, we need to find the relationship between c and s. We can do this by using the fact that the caterpillar overtakes the snail every time it completes one lap more than the snail.

Let's assume the number of laps completed by the caterpillar is n. Then the number of laps completed by the snail is n - 1.

The distance covered by the caterpillar in n laps is nC, and the distance covered by the snail in n - 1 laps is (n - 1)C.

Since the caterpillar overtakes the snail, the distance covered by the caterpillar must be greater than the distance covered by the snail: nC > (n - 1)C.

Simplifying the inequality, we get: C > C - C/n.

This implies that C/n > 0, which means n > 0.

Therefore, the caterpillar must complete at least one lap more than the snail: n > 1.

Now, let's substitute n = 3 into the equation C/c - C/s = 9 and solve for c and s.

Solution:

Substituting n = 3 into the equation C/c - C/s = 9, we get:

(3C)/c - (3C)/s = 9

Multiplying both sides of the equation by cs to eliminate the denominators, we get:

3Cs - 3Cs = 9cs

Simplifying the equation, we get:

9cs = 0

Since cs ≠ 0 (as given in the problem statement that the caterpillar and snail are moving), we can conclude that there is no solution to the equation.

Therefore, there is no fourth overtaking after the third overtaking.

Answer:

There will be no fourth overtaking.

Please let me know if you need any further clarification.