Question

К наполовину заполненному баку вместимостью 2,100 литров подведена труба через которую наливается по 230 литров воды каждый час. На дне бака образовалось отверстие через которое каждый час выливается 300 литров воды. Через сколько часов бак будет полностью пустой?

Answer 1

300-230=70(л) выливается каждый час
2100:70=30(ч)
Ответ через 30 часов бак будет пустым

Answer 2

Problem Analysis

We have a tank with a capacity of 2,100 liters that is initially half-filled. Water is being poured into the tank at a rate of 230 liters per hour, while water is being drained from the tank at a rate of 300 liters per hour through a hole at the bottom. We need to determine how many hours it will take for the tank to be completely empty.

Solution

To solve this problem, we need to calculate the net change in the water level in the tank per hour. The net change is the difference between the amount of water being poured into the tank and the amount of water being drained from the tank.

Let's calculate the net change in the water level per hour: - Water poured into the tank per hour: 230 liters - Water drained from the tank per hour: 300 liters

Net change in water level per hour = Water poured into the tank per hour - Water drained from the tank per hour Net change in water level per hour = 230 liters - 300 liters Net change in water level per hour = -70 liters

Since the net change in the water level per hour is negative (-70 liters), the water level in the tank will decrease by 70 liters every hour.

To determine how many hours it will take for the tank to be completely empty, we need to divide the initial water level in the tank (1,050 liters, which is half of the tank's capacity) by the net change in water level per hour (-70 liters).

Number of hours to empty the tank = Initial water level in the tank / Net change in water level per hour Number of hours to empty the tank = 1,050 liters / -70 liters Number of hours to empty the tank = -15 hours

Therefore, it will take approximately 15 hours for the tank to be completely empty.

Conclusion

In summary, if a tank with a capacity of 2,100 liters is initially half-filled and water is being poured into the tank at a rate of 230 liters per hour while water is being drained from the tank at a rate of 300 liters per hour, it will take approximately 15 hours for the tank to be completely empty.