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)

in 6 minutes the first tap will fill (12)(6) or 72 L
in the same 6 minutes the 2nd tap will fill (9)(6) or 54 L
for a total of 126 L
This is equal to 126 000 cm^3 (ahh, the beauty of the metric system)

volume of tank = area of base x height
= 2400h
= 126000
h = 52.5 cm

B)
During our 6 minutes we lost (2)(6) or 12 L
or 12000 cm^3
so 2400h = 126000 - 12000
h = 47.5 cm

A) To find the depth of water in the tank after both taps are turned on for 6 minutes, we need to calculate the total volume of water added by both taps and then divide it by the base area of the tank.

Tap 1 fills the tank at a rate of 12 L per minute for 6 minutes, so it adds a total of 12 L/min * 6 min = 72 L.

Tap 2 fills the tank at a rate of 3 L less per minute than Tap 1, so it fills the tank at a rate of 12 L - 3 L = 9 L per minute. In 6 minutes, Tap 2 adds a total of 9 L/min * 6 min = 54 L.

Therefore, the total volume of water added by both taps is 72 L + 54 L = 126 L.

To calculate the depth of water in the tank, we divide the total volume of water by the base area of the tank: 126 L / 2400 cm^2 = 0.0525 cm.

So, the depth of water in the tank after both taps are turned on for 6 minutes is approximately 0.0525 cm. That's quite shallow! You could use it as a fancy coaster.

B) If water leaks from the tank at a rate of 2 L per minute for 6 minutes, we need to subtract the total volume of water leaked from the total volume of water added to find the final volume. Then, we can divide the final volume by the base area to calculate the depth.

The total volume of water leaked is 2 L/min * 6 min = 12 L.

Subtracting this from the total volume of water added (126 L - 12 L), we get a final volume of 114 L.

Dividing the final volume by the base area of the tank (114 L / 2400 cm^2), we find that the depth of water in the tank is approximately 0.0475 cm.

So, after the water leaks for 6 minutes, the depth of water in the tank is even shallower than in part A, measuring approximately 0.0475 cm. If there were any fish in there, they would be having a hard time swimming!

Let's break down the problem step by step:

(A) What will be the depth of water in the tank after both taps are turned on for 6 minutes?

1. Calculate the total water filled by the first tap:
- The first tap fills the tank with 12 L of water per minute
- Therefore, in 6 minutes, the first tap will fill (12 L/minute) × (6 minutes) = 72 L of water

2. Calculate the total water filled by the second tap (which fills at a rate of 3 L less per minute):
- The second tap fills at a rate of (12 L/minute) - (3 L/minute) = 9 L/minute
- Therefore, in 6 minutes, the second tap will fill (9 L/minute) × (6 minutes) = 54 L of water

3. Calculate the total water filled by both taps:
- Total water filled = Water filled by the first tap + Water filled by the second tap
- Total water filled = 72 L + 54 L = 126 L

4. Calculate the depth of water in the tank:
- Volume of water = base area × depth
- Depth = Volume of water / base area
- Depth = 126 L / 2400 cm² = 0.0525 cm

Therefore, the depth of water in the tank after both taps are turned on for 6 minutes is approximately 0.0525 cm.

(B) If water leaks from the tank at a rate of 2 L per minute for 6 minutes, what will be the depth of water in the tank?

1. Calculate the total water leakage:
- The leakage rate is 2 L/minute
- Therefore, in 6 minutes, the total water leakage will be (2 L/minute) × (6 minutes) = 12 L

2. Calculate the remaining water in the tank after leakage:
- The total water filled by both taps is 126 L (as calculated above)
- Subtract the water leakage from the total water filled: 126 L - 12 L = 114 L

3. Calculate the depth of water in the tank:
- Depth = Volume of water / base area
- Depth = 114 L / 2400 cm² = 0.0475 cm

Therefore, the depth of water in the tank after 6 minutes, considering the 2 L/minute leakage, is approximately 0.0475 cm.

To find the depth of water in the tank after a certain amount of time, we need to gather the necessary information and calculate using the given data.

(A) To find the depth of water in the tank after both taps are turned on for 6 minutes, we need to calculate the total volume of water added by both taps, and then divide it by the base area of the tank.

1. Calculate the volume of water added by the first tap:
Volume of water = water flow rate x time
Volume of water = 12 L/min x 6 min = 72 L

2. Calculate the volume of water added by the second tap:
As mentioned, the second tap can fill the tank at a rate of 3 L less per minute compared to the first tap.
So, water flow rate of the second tap = 12 L/min - 3 L/min = 9 L/min
Volume of water = water flow rate x time
Volume of water = 9 L/min x 6 min = 54 L

3. Calculate the total volume of water added by both taps:
Total volume of water = volume from the first tap + volume from the second tap
Total volume of water = 72 L + 54 L = 126 L

4. Calculate the depth of water in the tank:
Depth of water = Total volume of water / base area of the tank
Depth of water = 126 L / 2400 cm^2
Depth of water = 0.0525 cm

Therefore, the depth of water in the tank after both taps are turned on for 6 minutes is approximately 0.0525 cm.

(B) To find the depth of water in the tank after water leaks out for 6 minutes, we need to subtract the volume of water leaked from the total volume of water added by the taps.

1. Calculate the volume of water leaked from the tank:
Volume of water leaked = water leakage rate x time
Volume of water leaked = 2 L/min x 6 min = 12 L

2. Calculate the adjusted total volume of water in the tank:
Adjusted total volume of water = total volume of water - volume of water leaked
Adjusted total volume of water = 126 L - 12 L = 114 L

3. Calculate the depth of water in the tank after leakage:
Depth of water = Adjusted total volume of water / base area of the tank
Depth of water = 114 L / 2400 cm^2
Depth of water = 0.0475 cm

Therefore, the depth of water in the tank after the tap water leaks for 6 minutes is approximately 0.0475 cm.