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.
(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?
B. D = 126 L - 2L/min * 6 min,
D = 126 - 12 = 114 Liters.
(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.