an empty rectangle tank with a base area of 2400 cm^2 is filed with water from 2 taps. one tap can fill the tank with 12L of water per minute, while the other tap can do it at 3l less perminute.
(A) what will be the depth of water in the tank after both taps are turned on for 6 minutes?
(B) if water leaks frome the tank at a rate of 2L per minute for 6 minutes, what will be the depth of water in the tank?
A. W = Rate * Time = (12 + 9)L/min * 6 min = 126 Liters..
B. D = 126 L - 2L/min * 6 min,
D = 126 - 12 = 114 Liters.
To solve these problems, we need to consider the volume of water that flows into the tank and the volume of water that leaks out of the tank.
(A) To find the depth of water in the tank after both taps are turned on for 6 minutes, we first need to calculate the total volume of water that flows into the tank during that time.
The first tap fills the tank at a rate of 12 L per minute, so in 6 minutes, it will fill the tank with 12 L/min * 6 min = 72 L.
The second tap fills the tank at a rate 3 L less than the first tap, so it fills the tank at (12 L/min - 3 L/min) = 9 L per minute. Similarly, in 6 minutes, it will fill the tank with 9 L/min * 6 min = 54 L.
Therefore, the total volume of water flowing into the tank in 6 minutes is 72 L + 54 L = 126 L.
Next, we need to find the height of the water in the tank. Since the base area of the tank is given as 2400 cm^2, we can use the formula:
Volume = Base Area * Height
Given that the base area is 2400 cm^2 and the volume is 126 L, we need to convert the volume to cm^3, as follows:
Volume = 126 L * 1000 cm^3/L = 126,000 cm^3
Now we can solve for the height:
126,000 cm^3 = 2400 cm^2 * Height
Height = 126,000 cm^3 / 2400 cm^2 = 52.5 cm
Therefore, the depth of water in the tank after both taps are turned on for 6 minutes is 52.5 cm.
(B) To find the depth of water in the tank after water leaks from the tank at a rate of 2 L per minute for 6 minutes, we need to subtract the leaked volume from the total volume calculated in part (A).
The leaked volume is 2 L/min * 6 min = 12 L.
Therefore, the new total volume after the leak is 126 L - 12 L = 114 L.
Using the same formula, we can find the new height:
114,000 cm^3 = 2400 cm^2 * Height
Height = 114,000 cm^3 / 2400 cm^2 = 47.5 cm
Therefore, the depth of water in the tank after the leak for 6 minutes is 47.5 cm.