Question

в пруду растут кувшинуи.за сутки количество кувшинок увеличиваются в 2 раза.через 20 суток пруд полностью покрылся кувшинками.через сколько суток пруд на половину был заполнен кувшинками?

Answer 1

если через 20 суток весь пруд покроют кувшинки, то за 19 дней пруд будет покрыт в 2 раза меньше, соответственно на половину.

Ответ: 19 суток

Answer 2

Problem Analysis

We are given that the number of water lilies in a pond doubles every day, and after 20 days, the pond is completely covered with water lilies. We need to determine how many days it takes for the pond to be half-covered with water lilies.

Solution

Let's break down the problem step by step:

1. On the first day, there is a certain number of water lilies in the pond. 2. On the second day, the number of water lilies doubles. 3. On the third day, the number of water lilies doubles again. 4. This doubling process continues until the 20th day when the pond is completely covered with water lilies.

To find out how many days it takes for the pond to be half-covered with water lilies, we need to work backward from the 20th day.

On the 19th day, the pond is half-covered with water lilies because the number of water lilies doubles every day. So, if the pond is completely covered on the 20th day, it must be half-covered on the 19th day.

Similarly, on the 18th day, the pond is one-fourth covered with water lilies because the number of water lilies doubles every day. So, if the pond is half-covered on the 19th day, it must be one-fourth covered on the 18th day.

We can continue this pattern until we find the number of days it takes for the pond to be half-covered.

Let's calculate it step by step:

- On the 20th day, the pond is completely covered with water lilies. - On the 19th day, the pond is half-covered with water lilies. - On the 18th day, the pond is one-fourth covered with water lilies. - On the 17th day, the pond is one-eighth covered with water lilies. - On the 16th day, the pond is one-sixteenth covered with water lilies. - On the 15th day, the pond is one-thirty-second covered with water lilies. - On the 14th day, the pond is one-sixty-fourth covered with water lilies. - On the 13th day, the pond is one-hundred-twenty-eighth covered with water lilies. - On the 12th day, the pond is one-two-hundred-fifty-sixth covered with water lilies. - On the 11th day, the pond is one-five-hundred-twelfth covered with water lilies. - On the 10th day, the pond is one-one-thousand-twenty-fourth covered with water lilies. - On the 9th day, the pond is one-two-thousand-forty-eighth covered with water lilies. - On the 8th day, the pond is one-four-thousand-ninety-sixth covered with water lilies. - On the 7th day, the pond is one-eight-thousand-one-hundred-ninety-second covered with water lilies. - On the 6th day, the pond is one-sixteen-thousand-three-hundred-eighty-fourth covered with water lilies. - On the 5th day, the pond is one-thirty-two-thousand-seven-hundred-sixty-eighth covered with water lilies. - On the 4th day, the pond is one-sixty-five-thousand-five-hundred-thirty-sixth covered with water lilies. - On the 3rd day, the pond is one-hundred-thirty-one-thousand-seventy-second covered with water lilies. - On the 2nd day, the pond is two-hundred-sixty-two-thousand-one-hundred-forty-fourth covered with water lilies. - On the 1st day, the pond is five-hundred-twenty-four-thousand-two-hundred-eighty-eighth covered with water lilies.

Therefore, it takes 19 days for the pond to be half-covered with water lilies.

Answer

It takes 19 days for the pond to be half-covered with water lilies.