Question

Три девочки сделали уборку комнаты за 1/15 часа. Айзат уберет эту комнату за 15 минут, Динара за 10 минут. За сколько минут уберет Сания? ПОЖАЛУЙСТА ПОМОГИТЕ РЕШИТЬ С РЕШЕНИЕМ И ОБЪЯСНЕНИЕМ. Задача если что с учебника

Answer 1

Ответ:

за 12 минут Сания уберёт комнату

Пошаговое объяснение:

По условию, три девочки сделали уборку комнаты за 1/15 часа:

1/15 часа = 1/15 * 60 = 4 минуты

Примем работу по уборке комнаты за 1 (одна целая) часть, тогда:

1. 1 : 4 = 1/4 часть работы выполнят три девочки за 1 минуту

2. 1 : 15 = 1/15 часть работы выполнит Айзат за 1 минуту

3. 1 : 10 = 1/10 часть работы выполнит Динара за 1 минуту

4. 1/15 + 1/10 = 2/30 + 3/30 = 5/30 = 1/6 часть работы выполнят вместе Айзат и Динара за 1 минуту

5. 1/4 - 1/6 = 3/12 - 2/12 = 1/12 часть работы выполнит Сания за 1 минуту

6. 1 : 1/12 = 1*12 = 12 минут - за 12 минут Сания уберёт комнату

Answer 2

To solve this problem, we can first find the cleaning rate of each girl by taking the reciprocal of the time it takes for them to clean the room. Then, we can add up their cleaning rates to find the combined cleaning rate of the three girls. Finally, we can use the combined cleaning rate to determine how long it would take Sanya to clean the room alone.

Let's calculate the cleaning rates of each girl:

- The three girls cleaned the room in 1/15 hour, which is equivalent to 4 minutes. Therefore, their combined cleaning rate is 1/4 minutes per room.

- Aizat can clean the room in 15 minutes, which is equivalent to 1/15 hour. Therefore, Aizat's cleaning rate is 1/(1/15) = 15 rooms per hour.

- Dinara can clean the room in 10 minutes, which is equivalent to 1/10 hour. Therefore, Dinara's cleaning rate is 1/(1/10) = 10 rooms per hour.

Now, let's find the combined cleaning rate of Aizat, Dinara, and Sanya:

- The combined cleaning rate of Aizat and Dinara is 15 + 10 = 25 rooms per hour.

- Since the combined cleaning rate of the three girls is 1/4 rooms per minute, we can convert it to rooms per hour by multiplying it by 60: (1/4) * 60 = 15 rooms per hour.

- Therefore, the combined cleaning rate of Aizat, Dinara, and Sanya is 25 + 15 = 40 rooms per hour.

Finally, let's determine how long it would take Sanya to clean the room alone:

- Since Sanya's cleaning rate is unknown, let's represent it as x rooms per hour.

- We know that the combined cleaning rate of Aizat, Dinara, and Sanya is 40 rooms per hour.

- Therefore, we can set up the equation: x + 25 = 40.

- Solving for x, we find that Sanya's cleaning rate is x = 40 - 25 = 15 rooms per hour.

- Since Sanya's cleaning rate is 15 rooms per hour, it would take her 1 hour to clean the room alone.

Therefore, Sanya would take 60 minutes to clean the room alone.

I hope this helps! Let me know if you have any further questions.