Question

Одна труба заполняет басейн за 8 часов а другая за 10 часов.через сколько часов наполнится 3/5 басейна если будут включенны две трубы?

Answer 1

Пусть объём бассейна будет Z, тогда поток в первой трубе равен Z/8 (бассейнов в час=б/ч), а во второй трубе Z/10 б/ч. Если работают две трубы, то общий поток будет Z/8+Z/10=Z*(1/8+1/10)=Z*(5/40+4/40)=Z*9/40 б/ч.
Требуется налить не весь бассейн, а только 3/5, то есть требуется Z*3/5. Для этого умножим общий поток на неизвестное время х.
Получаем уравнение x*Z*9/40=Z*3/5, сократим на Z; x*9/40=3/5; x=3/5 * 40/9;
x=8/3 ч. И переводим в нормальное время. х=2ч 40 мин.

Answer 2

Problem Analysis

To solve this problem, we can use the concept of work rates. We know the individual rates at which each pipe fills the pool, and we need to find the combined rate when both pipes are working together. Then, we can use the combined rate to determine the time it takes to fill 3/5 of the pool.

Solution

Let's start by finding the individual rates at which each pipe fills the pool.

- The first pipe fills the pool in 8 hours. - The second pipe fills the pool in 10 hours.

To find the individual rates, we can use the formula: Rate = Work / Time.

The rate of the first pipe is 1/8 of the pool per hour, and the rate of the second pipe is 1/10 of the pool per hour.

Now, to find the combined rate when both pipes are working together, we can add their individual rates: Combined Rate = Rate of Pipe 1 + Rate of Pipe 2.

Combined Rate = 1/8 + 1/10.

Let's calculate the combined rate.

Calculation

Combined Rate = 1/8 + 1/10 Combined Rate = 5/40 + 4/40 Combined Rate = 9/40

So, the combined rate at which both pipes fill the pool is 9/40 of the pool per hour.

Now, we need to find the time it takes to fill 3/5 of the pool using the combined rate. We can use the formula: Time = Work / Rate.

Time to Fill 3/5 of the Pool

Time = (3/5) / (9/40) Time = (3/5) * (40/9) Time = 8/3 Time = 2.67 hours

Answer

It will take approximately 2.67 hours to fill 3/5 of the pool when both pipes are working together.