Question

Аквариум объёмом 54 м3 заполняется водой при помощи двух кранов. Первый кран работает 3ч, а второй-2ч.Какова пропускная способность первого крана, если 1м3 он заполняет на 1 мин медленнее, чем второй?

Answer 1

1 кран наливает 1 куб.м за x мин, по 1/x части в минуту,
а 2 кран за (x-1) мин, по 1/(x-1) части в минуту.
1 кран работал 3 ч = 180 мин, а 2 кран 2 ч = 120 мин.
180/x + 120/(x-1) = 54
Делим всё на 6
30/x + 20/(x-1) = 9
30(x-1) + 20x = 9x(x-1)
50x - 30 = 9x^2 - 9x
9x^2 - 59x + 30 = 0
D = 59^2 - 4*9*30 = 3481 - 1080 = 2401 = 49^2
x1 = (59 - 49)/18 = 10/18 = 5/9, но тогда x - 1 < 0 - не подходит.
x2 = (59 + 49)/18 = 108/18 = 6, x - 1 = 5
Ответ: 1 кран наливает 1 куб.м за 6 мин, а 2 кран за 5 мин.

Answer 2

Calculation of the First Tap's Flow Rate

To determine the flow rate of the first tap, we need to compare its filling time with that of the second tap.

Given: - Volume of the aquarium: 54 m^3 - First tap's operating time: 3 hours - Second tap's operating time: 2 hours

To find the flow rate of the first tap, we can compare the time it takes to fill 1 m^3 of water using each tap.

Let's assume that the second tap fills 1 m^3 of water in t minutes. Therefore, the first tap fills 1 m^3 of water in (t + 1) minutes, as it is slower by 1 minute.

To find t, we can use the equation:

2 hours = t minutes

Converting 2 hours to minutes:

2 hours = 2 * 60 minutes = 120 minutes

Therefore, the second tap fills 1 m^3 of water in 120 minutes.

Now, let's find the time it takes for the first tap to fill 1 m^3 of water:

1 m^3 = (t + 1) minutes

Simplifying the equation:

t = 1 - 1 = 0 minutes

Therefore, the first tap fills 1 m^3 of water in 0 minutes.

Based on the calculations, we can conclude that the first tap has a flow rate of 0 m^3 per minute.

Please note that the provided sources do not contain relevant information for this specific calculation.