Question

Первая труба может наполнить бассейн за 20 мин., вторая за 24, а третья за 30. За сколько минут неполнят бассейн 3 эти трубы вместе.

Answer 1

Какую часть бассейна наполняют трубы за 1 минуту - 1/20, 1/24 и 1/30.

Вместе за 1 минуту три трубы наполняют:

1/20 + 1/24 + 1\30 = 6/120 + 5\120 + 4/120 = 15/120 или 1|8.

Значит весь бассейн три трубы наполнят за 8 минут. 

Answer 2

Problem Analysis

We are given three pipes that can fill a pool in different amounts of time. The first pipe can fill the pool in 20 minutes, the second pipe can fill it in 24 minutes, and the third pipe can fill it in 30 minutes. We need to determine how long it will take for all three pipes to fill the pool together.

Solution

To find the time it takes for all three pipes to fill the pool together, we can calculate the reciprocal of the sum of the reciprocals of the individual pipe rates.

Let's denote the rates of the three pipes as follows: - Rate of the first pipe = 1 pool / 20 minutes - Rate of the second pipe = 1 pool / 24 minutes - Rate of the third pipe = 1 pool / 30 minutes

To find the combined rate of all three pipes, we add up their individual rates: Combined rate = Rate of the first pipe + Rate of the second pipe + Rate of the third pipe

To find the time it takes to fill the pool, we take the reciprocal of the combined rate: Time = 1 / Combined rate

Let's calculate the combined rate and the time it takes to fill the pool.

Calculation

The rate of the first pipe is 1 pool / 20 minutes. The rate of the second pipe is 1 pool / 24 minutes. The rate of the third pipe is 1 pool / 30 minutes.

The combined rate is the sum of the individual rates: Combined rate = 1/20 + 1/24 + 1/30

To calculate the combined rate, we need to find a common denominator for the fractions. The least common multiple (LCM) of 20, 24, and 30 is 120.

Converting the fractions to have a common denominator of 120: Combined rate = (6/120) + (5/120) + (4/120) = 15/120 = 1/8

The combined rate is 1/8 pool per minute.

To find the time it takes to fill the pool, we take the reciprocal of the combined rate: Time = 1 / (1/8) = 8 minutes

Answer

It will take 8 minutes for all three pipes to fill the pool together.

Explanation

When the three pipes work together, their combined rate is 1/8 pool per minute. This means that they can fill 1/8 of the pool in 1 minute. Therefore, it will take 8 minutes for them to fill the entire pool.