Question

Нужно подробное решение. Первый насос наполняет бассейн за 8 ч., а второй насос выкачивает всю воду из бассейна за 18 ч.. Считая , что скорости работы насосов постоянны, определите, за какое время будет наполнен этот бассейн, если он пустой, и оба насоса начнут работать одновременно.

Answer 1

Первый насос за час заполняет 1/8 бассейна, а второй выкачивает 1/18 бассейна. тогда если они будут работать одновременно, то бассейн будет заполняться со скоростью 1/8-1/18=9/72-4/72=5/72
тогда время, за которое бассейн заполнится полностью = 1/(5/72)=72/5= 14 часов 24 минуты

Answer 2

Problem Analysis

We are given two pumps: the first pump fills the pool in 8 hours, and the second pump empties the pool in 18 hours. We need to determine how long it will take to fill the pool if both pumps start working simultaneously.

Solution

To solve this problem, we can use the concept of rates. Let's assume that the rate at which the first pump fills the pool is R1 (in pools per hour) and the rate at which the second pump empties the pool is R2 (in pools per hour).

Since the first pump fills the pool in 8 hours, its rate can be calculated as R1 = 1/8 pools per hour. Similarly, since the second pump empties the pool in 18 hours, its rate can be calculated as R2 = 1/18 pools per hour.

Now, when both pumps are working simultaneously, their rates add up. So, the combined rate of filling the pool can be calculated as R = R1 - R2.

To find the time it takes to fill the pool, we can use the formula Time = 1/R.

Let's calculate the values:

R1 = 1/8 pools per hourR2 = 1/18 pools per hour R = R1 - R2 = (1/8) - (1/18) pools per hour

Now, let's calculate the time it takes to fill the pool:

Time = 1/R = 1 / ((1/8) - (1/18)) hours

Calculation

To calculate the time it takes to fill the pool, we need to find the reciprocal of the difference between the rates of the two pumps.

Time = 1 / ((1/8) - (1/18)) hours

Using the formula for the difference of fractions, we can simplify the expression:

Time = 1 / ((9/72) - (4/72)) hours

Time = 1 / (5/72) hours

To divide by a fraction, we can multiply by its reciprocal:

Time = 1 * (72/5) hours

Time = 72/5 hours

Answer

Therefore, it will take 14.4 hours to fill the pool if both pumps start working simultaneously.

Conclusion

In conclusion, if the first pump fills the pool in 8 hours and the second pump empties the pool in 18 hours, it will take 14.4 hours to fill the pool if both pumps start working simultaneously.

Please let me know if I can help you with anything else.