Question

Через кран в бассейн вливается в минуту 300 л воды, а через трубу для стока вытекает 8400 л в час.Если работают одновременно кран и сток, бассейн наполняется за 12 ч.За какое время наполниться бассейн если закрыть сток?

Answer 1

1 ч=60 мин

300*60=18000 л вливается за 1 час

18000-8400=9600 л остается в бассейне за 1 час

9600*12=115200 л в бассейне всего воды

115200:18000=6,4 ч

Ответ : за 6,4 часа

Answer 2

Problem Analysis

We are given that water flows into a pool at a rate of 300 liters per minute through a faucet, and water flows out of the pool at a rate of 8400 liters per hour through a drain. We need to determine how long it will take to fill the pool if the drain is closed.

Solution

Let's first convert the flow rates to the same units. Since the faucet flow rate is given in liters per minute and the drain flow rate is given in liters per hour, we need to convert the drain flow rate to liters per minute.

To convert liters per hour to liters per minute, we divide by 60 (since there are 60 minutes in an hour).

The drain flow rate is 8400 liters per hour, so the drain flow rate in liters per minute is:

8400 liters/hour ÷ 60 minutes/hour = 140 liters/minute

Now that we have both flow rates in liters per minute, we can calculate the time it takes to fill the pool.

Let's assume the volume of the pool is V liters.

When the faucet and drain are both open, the net flow rate into the pool is:

300 liters/minute - 140 liters/minute = 160 liters/minute

We are given that it takes 12 hours to fill the pool when both the faucet and drain are open. Since there are 60 minutes in an hour, the total time to fill the pool is:

12 hours × 60 minutes/hour = 720 minutes

Using the net flow rate, we can calculate the volume of water that flows into the pool in 720 minutes:

Volume = Flow rate × Time

V = 160 liters/minute × 720 minutes

Now, we can solve for the volume of the pool:

V = 115,200 liters

Therefore, the volume of the pool is 115,200 liters.

If we close the drain, the net flow rate into the pool will be equal to the flow rate from the faucet, which is 300 liters per minute. We can use this flow rate to calculate the time it takes to fill the pool with the drain closed.

Time = Volume ÷ Flow rate

Time = 115,200 liters ÷ 300 liters/minute

Time = 384 minutes

Therefore, it will take 384 minutes to fill the pool if the drain is closed.

Answer

If the drain is closed, it will take 384 minutes to fill the pool.