Question

Дашина собака Бобик разгрызла учебник по математике на несколько кусков. Даша решила склеить учебник. За минуту она склеивала вместе три куска (начальных или ранее склеенных). В результате учебник стал вновь целым за 36 минут. За какое время учебник стал бы целым, если бы Даша работала аккуратнее и склеивала вместе за минуту не по три, а по два куска?

Answer 1

Ответ:

1) 36×3=106 ( всего кусков)

2)106÷2=53 минуты

Answer 2

Problem Analysis

In this problem, Dasha's dog, Bobik, chewed up her math textbook into several pieces. Dasha decided to glue the pieces back together. Initially, she glued together three pieces per minute, whether they were original pieces or previously glued ones. After 36 minutes, the textbook was whole again. We need to determine how long it would take for the textbook to become whole if Dasha glued together two pieces per minute instead of three.

Solution

Let's analyze the problem step by step:

1. Initially, the textbook was in several pieces. 2. Dasha glued together three pieces per minute, whether they were original pieces or previously glued ones. 3. After 36 minutes, the textbook was whole again.

To solve this problem, we can work backward from the moment the textbook became whole again. Let's assume that it took x minutes for the textbook to become whole if Dasha glued together two pieces per minute.

1. After x minutes, Dasha glued together two pieces per minute. 2. After (x-1) minutes, Dasha glued together two pieces per minute. 3. After (x-2) minutes, Dasha glued together two pieces per minute. 4. And so on, until we reach the initial state of the textbook.

We can see that the number of glued pieces decreases by one every minute. So, after 36 minutes, the number of glued pieces would be 36 less than the initial number of glued pieces.

Let's calculate the initial number of glued pieces: - Dasha glued together three pieces per minute, so the number of glued pieces after 36 minutes would be 3 * 36 = 108.

Therefore, the initial number of glued pieces was 108.

Now, let's calculate how long it would take for the textbook to become whole if Dasha glued together two pieces per minute instead of three.

1. After x minutes, Dasha glued together two pieces per minute. 2. After (x-1) minutes, Dasha glued together two pieces per minute. 3. After (x-2) minutes, Dasha glued together two pieces per minute. 4. And so on, until the number of glued pieces reaches 108.

We can see that the number of glued pieces increases by one every two minutes. So, the time it would take for the textbook to become whole if Dasha glued together two pieces per minute can be calculated as follows:

- The number of glued pieces increases by one every two minutes, so the time it would take for the textbook to become whole is 108 * 2 = 216 minutes.

Therefore, if Dasha worked more carefully and glued together two pieces per minute instead of three, it would take her 216 minutes to make the textbook whole again.

Answer

If Dasha worked more carefully and glued together two pieces per minute instead of three, it would take her 216 minutes to make the textbook whole again.

Note: The solution provided above is based on the given problem statement and assumptions made during the analysis.